I think that there's nothing wrong with red oak boards, especially when you're on a budget. You can get a nice bow if you start with a decently cut board, and for the price you can't beat it. I made the mistake of investing in a few hickory staves to start with, and after screwing up all three I ended up with $150 less cash than I started with and no usable bow. Another option might be to try and harvest some wood locally, but I don't know how easy that is for you.
In my experience a red oak board will give you a fine bow, and linen backing it will help it hold up even if the board wasn't sawn perfectly with the grain. Making the limbs wider, say 2-1/2 inches or so, wouldn't hurt, although if you want to take a crack at a pyramid-style bow I'm sure that would work too. If you're worried about string follow, I'd reflext the limbs just a bit near the handle. You'll probably get some string follow no matter what, but a little doesn't hurt anything. The 1-3/4 inch wide ash flat bow I'm hunting with this year ended up with about an inch of string follow, and still tosses arrows with authority!
Best of luck!
-Eric