Hey there, do you have in mind what kind of bike you're looking to use?
Here's a thread with some good info:
http://motorbicycling.com/showthread.php?t=42886
You might want to be more specific about what you want to do. A lot of people will mention the
Harbor Freight 79cc engine, there are lots of build threads on here that you could follow that use that engine. From what I know, the HF 79cc is a pretty hard build.
People will probably bring up the
Huasheng 142F, great engines but on the lower-quality spectrum because of the cheap price tag. If you haven't already I would do some research on those bad-boys, but for your situation it's probably not the best bet.
Since you have a hefty budget, I would say go for a nice
Honda engine. I'm assuming you want to do an in-frame build, but may I suggest a friction drive? Those are the easiest to install and very easy to maintain. Staton inc sells a solid
Honda Friction Drive kit for about $350. With your budget you could buy that kit, and a nice mountain bike and you could finish your build in one afternoon.
Although I do admit a friction drive build would be quite boring and possibly "too easy"...anyway good luck on your build I hope I helped!