So what is so wrong with the Kawasaki that makes it not worth repairing?
$300 is cheap for a major brand bike that runs. If it shifts through all the gears, the wheels are reasonably round, the forks are straight and the engine runs at all I would expect that it would be worth repairing.
You didn't provide any dollar figure on your budget, but since a helmet and boots seems to be an issue I would guess that buying a brand new bike is out of the question.
If you are going to take it to a shop for every significant repair/maintenance item that comes up then buying new (or at least newer) would be a really good thing. With a new bike you are at least starting with a good base. If you don't maintain it, however, it will lose a lot of value fairly quickly.
If you are buying a used bike then you should expect to spend some money fixing it up and keeping up on the maintenance. A MX bike will have a high performance engine that needs significant maintenance to keep them running properly. Rebuilding the top end (piston & rings) is recommended after only 20 hours of use. You can often let it go a lot longer but if you wait until it fails a $150 top end rebuild can turn into a $1500 rebuild.
Likewise on chains & sprockets. They wear out, and if you change them before something breaks it is $100. If the chain breaks and jams into the engine case it can totally destroy the engine.
When you buy another used bike be sure to ask the seller how long it has been since the top end was rebuilt. If it has been a long time, or the seller can't tell you when it was rebuilt last, assume it needs one ASAP.
Like YZ_rider said, a 125cc two stroke MX bike would be a good bike. Buy as new as your budget will allow. Be sure to leave some budget for repairs and additional riding gear (knee pads, chest protector, gloves, goggles)
Rod