You ask/You answer: What's the best project bike?

At my local motocross course you'll find many of the young riders are still hammering about on two strokes. They do so because they are cheaper to buy, still outperform four strokes of similar and larger capacities are lighter and hence easier to handle and have good and cheap parts availability. In short they are more fun. 

For example there's no problem getting cheap spares for something like an eighties CR125 with it's punchy 31bhp engine. However the much newer CRF150  can't be had cheaply, used spares are rare and the engine only delivers 24bhp.

If you're looking at competition then four strokes have an advantage in certain classes, indeed some classes only allow four strokes. However there is still plenty of racing where two strokes have the upper hand or are the only  bikes allowed. If you're not considering competition then what you're looking at is the most fun per pound spent. And a two stroke is easilly going to win out on that basis.

Somebody else mentioned the likes of the TY125 (although I'd go for the more plentiful 175) and there are no problem getting spares for those and they are ancient.