2 strokes need good rings and a good round cylinder wall to be able to seal , as stated in the last post have the cylinder checked for size , it should be within spec , ie. if std size is 50mm your manual will give the tolerance that this bore should fall within , also you should check for tapered cylinder walls as well as out of roundness , you shouldn't see any more than a couple of tenths (.0002)
I have seen 2 strokes that will run like yours and the repair is just a new set of rings sometimes . although if it were my bike I would at least do rings piston wrist pin and needle bearings for wrist pin . any good piston company usually gives you everything when you buy a piston .
cylinder work is going to cost you ,if its an old design , ie no plated bore than you can have the cyl. bored and honed to the next size up , usually they go in increments of .010 , .020 , .030 , .040 would not suggest boring over .040 .
I would see what is available for piston and rings 1st and then decide , also previous owner could have already had the jug bored .
the cylinder is what needs to be carefully checked out b4 you start , if its still in spec than just a simple piston and ring replacement will make the yammie run like new again . if the cylinder is junk you could very likely end up with a expensive repair bill and will need to decide if it is worth that much to repair or use the money to buy another used dirt bike .
I'm guessing that if the engine is shot the rest of the bike has been ridden hard also !
It aint rocket science but two strokes do need a good seal in the cylinder to be able to deliver fuel (suction)and also needs that same cylinder seal to produce HP under the fire stroke !