The good news is that they all seem to charge around the same thing. The bad news is it is north of $160. My sample size is small but over 20 years I have used 3 different companies and have talked to many other homeowners about whom it is that they have used. Roto rooter and others advertise $99 or something like that but somehow always wind up charging $160.
Russ's advice is good. Avoid using lye (liquid plumr etc) if you can. I also prefer to use a big stew pot that can hold a few gallons of boiling water. I have burned myself doing this but that just gets mixed up with all the other burns and tattoos on my hands and arms.
Most clogs can be handled by even the most incompetent "not so handymen" including myself. As a matter of fact, it's one of the few things I do around the house myself.
There are different models of snakes available that are inexpensive. I have a hand shake that goes about 4 feet in to a pipe that works well most of the time. I also have a 20ft snake that fits on the end of a drill or can be hand cranked that works ok.. Doing both the boiled water and snake have worked very well for me. The snakes cost around $20-$50. Before you even try that use a wire hanger and see what happens.
There are alos various combinations of salt, boiled vinegar and bkaing soda you can try. Try google as I don not remember the proportions.