I would strongly recommend you read this page:http://www.geology.smu.edu/~dpa-www/robo/nbot/
There are a couple dozen links at the bottom of the page to other two-wheel balancing robots.
That should give you a better idea of what is required and what isn't, and what parts will work. Which microcontroller you use isn't going to make a lot of difference.
Check out these places:http://www.bdmicro.com/http://www.newmicros.com/
for some options.
I personally have a couple Tiny2138 ARM boards, which are awesome - 60 MIPS, full 32 bit processor, free C compiler, dual PWM channels, in a tiny footprint, for $69. The 2131 has a lot less memory, but most of the same other features, for $29 !!! Note that these boards are 3.3 volts, which may or may not be an issue interfacing with some sensors and motor controllers.
As far as making your own boards, what I typically do is buy a blank proto-board from Radio Shack, and solder wires underneath. You can see an example of that here:http://www.huv.com/miniSumo/seeker3/
The 5th and 6th pictures show the top and bottom of the controller board I soldered.
You can lay out a PCB and have them professionally printed as well, but I wouldn't advise that until you have a lot of experience putting this stuff together, so you know ahead of time exactly what is needed.