It's SO MUCH FUN to brainstorm with other people! Especially when it comes to Star Wars. :D
I'm not really sure how many star systems are in the Republic, either; I think I remembered reading the "one million" amount somewhere, and that's what I've used. Personally I think that's a little bit TOO big, and I would prefer a number somewhere in the lower thousands, myself. And like you said, it would still make it easy for the Republic to create an army out of all the member worlds in a very short amount of time.
And yes, Anakin HAS to be from Tatooine. I don't think it would hurt things too much; it would make Tatooine's appearence in ANH less "random" if we've seen it before, essentially. That was one of the things that the PT actually did get right - but executed EXTREMELY poorly.
Plus, things can change on Tatooine a lot, ESPECIALLY if you make the gap between conflicts wider. We can first see Tatooine circa 35 BBY, when Anakin meets Obi-Wan, and it can seem a lot different from years later. Then we'd only see it again briefly in the third episode, when Obi-Wan drops off Luke and goes off into the desert, so we wouldn't really see how much it's changed until ANH. The cantina scene can still have a "wow factor," but of a different sort. Instead of "ooh this place is exotic and cool!" upon seeing it in ANH (after seeing it in our theoretical prequels), the audience might think "ooh, look how much this place has changed!"
What do you guys think of that? Let's toss some more ideas around!