All in a rider minibike for $300 or less is doing well. $500 is more realistic. Vintage correct restoration or performance $1,000+
The little things add up fast...clutch, carb kit, gas line, spark plug, head gasket, chain, recoil spring/rope, air filter, oil, muffler, cables, tires, tubes, seat, throttle grips, bearings etc...
Look for an old 5hp Tecumseh horizontal engine from a snow blower or Roto-tiller with a 3/4" PTO shaft for as cheap as you can if not free. Rebuild the carb, clean/set the points and do whatever to get it running. Any other junk small engines you find for free disassemble noting all the parts, how they work together and why you think it failed.
Get some books on small engines and read them like a novel
If you can repair/tune an old Tecumseh to start on 1st pull, idle like an old pocket watch and rev without hesitation you are on track to tackle any engine.