The list of things to check could get quite long if you were going to get fussy I guess.
As far as actually riding the bike is concerned:
Check sprockets and chain. Especially check for tight link joints by making sure the entire chain wraps nicely around the front sprocket without lifting off.
Check the fork seals are not leaking. It is pretty simple to replace the front fork oil. If on a budget just use cheap Automatic Transmission Fluid. It will be a lot better than the old oil.
Check wheel bearings
Check steering head bearings
Make sure brakes are working well.

I guess it is also worth pulling the fuel tap apart and cleaning it out. And check that the fuel hose from tank to carbies is in good condition.
Make sure that fuel does not run out of the carby overflows when the fuel tap is on. If it does then check needle valves and float heights
Maybe drain the two stroke oil tank and check that the oil light comes on.