I have extensive experience with avoiding sugar. I had to cut it out completely for a while, then was able to consume it in small amounts. Also, I love cooking and enjoy baking. So...this may not be a welcome answer, but it's based in experience.
Substitutes: Often expensive and nutritionally suspicious, and most of them don't work in baking. Sugar is important in certain baked goods because it browns the tops of cookies, turns into caramel, reduces to syrup, etc; most other sweeteners lack these crucial chemical properties. Splenda is reportedly best for baking, but I wouldn't want to make it a regular part of my diet. I've heard of folks who use half sugar and half Splenda, and if that appeals to you, go for it. Some strict sugar-avoiders recommend xylitol, but it's also kind of weird and not ideal for baking. (I've tried it and it's not bad, but it imparts a cooling sensation and like the other -ol sweeteners it can have a laxative effect, which kind of undermines the joy of baked goods.) Stevia is useless for baking. If your doctor says it's okay there are plenty of natural sugars like date, palm, honey, maple, etc, but I suspect that for your purposes they're still sugar, and they cost more than cane/beet, which is rough when you need a bunch for cookies.
So honestly? If you're a frequent baker, I'd suggest using real sugar, but way way less than the recipe calls for. Cut the sugar down by half or even two-thirds, and don't expect other people to love what you bake (though sometimes they surprisingly do, as with the gluten-free, half-sugar cookies I made tonight). This may change the texture of some items, because you're removing bulk from the recipe and losing some of what sugar does chemically, but it's not always a problem (my cookies are a bit cakier than the photos in the recipe show, but they're definitely cookies). You'll just have to experiment.
By the way, if you're going to go this route, you may find that your reduced-sugar recipes just aren't sweet enough! If this is true, you have to adjust your taste too. Stop eating sugar entirely (no dried fruit, no juice, nothing sweet) for like a month. When I did it, the first few weeks were torture--I was craving sweets nonstop, and suddenly the hippie-alternative notion that we're addicted to sugar made sense to me. I mean, if you're young and healthy and don't want anyone to tell you not to eat ice cream for dinner, that's totally cool; I wasn't healthy and I had no choice, and in the long run I'm grateful that I no longer want to eat entire bags of Sour Patch Kids. Anyway, the crazy cravings do vanish, and then you can experiment with lower-sugar recipes to your heart's content. And your doctor will love you.
As for fat, I can't help you there, but there's a lot out there about substituting fruit pastes and such, along with stuff about better fats in other answers here.