I'm just now finishing up my new bike build. I have about $200 in it.
I got lucky and found a bicycle by a dumpster. It was nearly new and only needed the tires pumped up. It was in such good shape that I had the police run the serial numbers to see if it was stolen. I spent $155 (with shipping) for a 50cc Grubee Starfire Gen II engine from USABikemotors.com because I heard grubee had a good reputation for being a good motor. I also bought a big Schwinn cruiser seat from K-mart for $25. the rest was in spray paint, better spark plug and wire, a better fuel line, and fuel filter.
Thrift stores, Craigslist, Trash piles, and even pawn shops are good places to get cheap bikes. I got a 1973 schwinn collegiate bike from the thrift store for ten bucks. I bought new tires online from amazon.com for $30. After lots of elbow grease, shining chrome, taking the bearings apart, cleaning them, and repacking with fresh grease, I ended up with a bicycle engine candidate for a total cost of $40 to me. I decided to keep it original for the time being.
My point is, if you are handy with tools and you keep your eyes open for a good bike you can get rolling for cheap. I bought and sold stuff on craigslist for a while in order to get $$$ for my first engine.
www.thatsdax.com has a 49cc engine for $98 plus shipping. Probably the lowest Ive seen besides Ebay.
If you go with a Grubee engine. The 50cc one has a steel sleeve which suggests longer life to me. Chrome bores are good too but I understand there has been quality issues with some of the more recent ones.
A good rule, is to buy from places where you can get spare parts also.