I want to answer your question with a discussion about various bird species, but first have to say that, in general, birds have the ability to live much longer (given proper care) than typical household pets. Even a budgerigar obtained now (AKA a budgie or parakeet) could be alive and well, living in your home when you son packs off for college. I could give my African Grey to J's grandchild who is just a few years older than the bird and she could have that bird when she reaches her 50th birthday (and beyond). Depending on your outlook on being responsible for animals you adopt (health, well-being, happiness, and longevity) this decision based on your very young son's current fascination may be a bit premature, but I trust you will consider all the facts (as you have had some bird experience and are willing to ask the right questions).
So, if not a real bird right away, then what?
There are some really neat little stuffed animal birds that are quite nicely realistic (but plush) that have a little device in them with the recorded bird song and when you squeeze them just right they play for a couple of cycles of the song. Here are some examples. I remember seeing them for a time in REI but certainly they are available through many online sources.
Having a window based or close bird feeder can bring local birds right up to your kitchen or dining room window and can be very entertaining. If you plant your garden with the right bushes and plants you can attract a huge variety of local native birds to where you can watch them very close by. Hummingbird feeders are also very successful for getting such amazing birds in close to see from inside your house. You have to learn to be very still when wild birds are nearby so you can observe them without scaring them away. Having a feeder through the winter months is a commitment not to take lightly, as birds will come to depend on that source of food as part of the resources of their range. Keeping it clean and providing high quality food is important.
Obviously there is a huge gamut of DVDs (watching a video screen for any length of time is probably not recommended in a very young child) for seeing high quality movies of real birds and hearing their song. For adults, Winged Migration will absolutely blow your mind as you watch birds up close in formation flight (some at high altitude) - you gotta see it to believe it, and then you will wonder how they did it (video explanation is included).
Then there are zoo exhibits to go to where you can go into a flighted bird aviary and have birds right around you coming to eat on seed sticks given to visitors. The Point Defiance Zoo & Aquarium has such an exhibit called Budgie Buddies that is in its last couple weeks of activity before closing for the season (call as it is weather permitting). Go right away if you are interested.
There are also breeder and exhibitor shows that you can go to (see below, one coming up this weekend).
So, now to real birds in your own home.
If you are convinced that having some real live birds of your own is what you want, then you have the choice between the finches, canaries or small psittacines, that is the smaller parrot species like budgerigars, parrotlets (pronounced PARRO-lets), cockatiels, etc. Up front I will have to admit that I am not very well versed in finch and canary knowledge and urge that for whatever species of birds you may consider, to look for folks that already own or breed them and go to that source for the best information.
Here is a very timely resource. Cascade Canary Breeders Association Their fall bird (finch and canary) show is this coming weekend and family admission price is $5. I believe they also have a large show in the spring of each year.
Social finches like zebra finches have a huge following (there are two currently up for adoption on the QL classidfieds) and you could learn more about them at the resource above.
Going to a show like that referenced here can be a good way to see up close various species and also get great information about local resources and talk to experienced owners. It is easy to dismiss the smaller birds as not having significant intelligence, distinct personalities, and desire to communicate with the humans they live with. I may have thought that of canaries, but after going to a bird club meeting on the peninsula last year, that all changed. A member brought one of his small hand raised white (flighted) canaries. As the meeting went on the bird started with the person immediately to the person's right and visited them on their hand, shoulder, chattering in their ear and being very interactive and socially curious. That continued for everyone seated around the large ring of tables, as the bird flew to each one in order, including me, spending a few minutes with each person, eventually returning to their owner.
You need to go and look at real birds to know more about the amount of space you will need to dedicate to keeping them, the mess involved, and the amount of noise they can make. Obviously for smaller birds it might seem that their needs would be less but you can't make that assumption. Canaries and finches are perching birds and need much more horizontal space to be properly active and happy. They jump and fly from perch to perch and need cages that are longer horizontally than high so they have appropriate movement space. Psittacine birds have feet and a beak designed for grasping and can climb around their enclosures as well as use their wings. Their cages can be more square and with different play, perching areas at various heights. Larger enclosures are always preferable for activity and need to be outfitted with lots of perching options as well as hanging and side mounted toys for play and activity. For mixed sex groups of budgies you have no real worry about breeding as long as you don't provide anything that can be used as a nestbox.
Canaries and finches sing and make other noises that vary according to their species and sex. Budgies have a pleasant sound/whistles and actually are quite capable of learning to talk (I had a grandfather with a budgie that he had taught to say its name and the home phone number - for recovery, if he accidentally got outside).
Beyond those options you have cockatiels, parrotlets, and the Pyrrhura conures. Cockatiels are larger birds and make wonderfully and quite long lived pets. It is not unusual to meet folks with cockatiels that are in their twenties. They certainly require significant time and attention (as all birds do, they aren't potted plants). Parrotlets are often described as full size parrots in small bodies and I believe it after hearing the stories of people that own them. These species are a significant leap in investment of time and energy to keep. Most folks don't really understand how much attention and time companion birds require. In general, I would recommend against parrotlets and lovebirds (which I have not discussed here) as being too challenging and not well suited to being handled by a small child. If your child is somewhat older when you make the bird decision you may want to consider a Green-cheeked Conure as a family bird. They are one of the quieter conure species (genus Pyrrhura versus genus Aratinga), but yet another leap up in longevity (with 30+ years possible).
The interaction between your child and the birds must be strictly chaperoned. Small birds can be quite fragile in a confined space and a child erroneously trying to discipline a bird by striking the cage or moving too quickly even once could send a bird in fright to a collision and severely bad injury.
With budgies, having a couple to serve as cage buddies or even a small colony of three or more in one enclosure is quite possible and being the social beings they are will hang out, communicate and allo-preen each other. You need to have plenty of feeding stations and place multiple groups of veggies and other treats so no one bird can garner the supply from others. Keeping an eye on the group dynamics is a good idea and spend time each day watching each bird to assess its health state is a good practice. With a group it is easy to miss that one or another is less active or may have an injury that needs attention.
Any bird needs out of cage time to be social with the humans and enjoy the freedom of flight and movement. Clipping wings on small birds can be problematic. Lovebirds (for example) are short tailed birds and fly very well even with primary flight feathers clipped. Budgies are actually long tailed parrots and have a different flight dynamic. They can be very unstable with clipped wings and falls to the floor can be quite traumatic. Clipped wings are meant to be done so that a bird can fly with control down (but not gain altitude). With such small birds getting that balance can mean a very slight difference in the clip. Clipping bird wings (that is, trimming flight feathers that have no feeling or enervation and are molted periodically and replaced) is one of the many hotly debated issues in keeping birds as pets. All of my parrots are fully flighted and fly in my home. Having flight capable budgies could work very well in a regularly used space (the birds get to know the flying space, available landing spots) and will actually hang out on the top of their cage and return to eat and rest after exercise. Having out of cage time coincide with time to manage the cage cleaning chores and replenishing food and treats can be a good daily occurrence. Having regular interaction time and finger time (bird perched on hand), gentle touching (scritches on the head and neck) will keep your birds interacting with you and seeking your attention.
All birds deserve meticulously clean living environments which generally means daily cleaning chores (both in and around cage areas), replenishment of clean water, provision of fresh and pelleted food, not just seed (seed is nutritionally deficient as a single food and will promote poor health and shortened lifespan), fresh or well filtered air and good full spectrum lighting.
All birds deserve appropriate veterinarian care and budgies in particular require vaccination for Polyomavirus. We are particularly fortunate in this area to have a number of highly qualified certified avian vets in the western Washington and Puget Sound region. If you need more information or references, please contact me directly.
All birds will require in house or exterior sitting services if you will be away from them for more than 24 hours. Know that some folks with larger psittacine birds will not want to sit your budgies as they can be carriers of some diseases that can affect other species. You can have a somewhat smaller and transportable "away cage" ready for those times (still needs to be outfitted with toys and such) that the birds can be happy in for a short stay.
There is another whole issue I won't try to discuss here on the home environment and changes that you need to make to ensure bird health indoors (getting rid of teflon pans in the kitchen, not using aerosols, having a good air filter etc.). However, you should also be aware that birds create allergens (dander and feather dust) that can be a problem for people with asthma or other reactive breathing difficulties. These conditions by anyone in your home and especially in your son would make having birds a real problem and probably not a good choice.
Although I hate the titles of these series, the books written for "dummies" and "complete idiots" on the various pet bird species can be good general guides. There are lots of good books on keeping birds. Pay attention to copyright dates so you are reading relatively recent literature and always consult more than one source as philosophy and opinions on best practices can vary. It is THE BEST practice to fully understand what you are getting into when considering having birds as pets BEFORE obtaining them.
In summary, go see birds where you can, meet folks that have birds and talk to them (bird clubs and bird shows), read books on keeping birds (use the library as a start), and ALWAYS consider taking in birds that need new homes (there are plenty), contact me for references, if you need.
If you understand the commitment ahead of time and have the facts you will be ready to meet the challenges and enjoy a long satisfying relationship with wonderfully interesting feathered beings in your life.