The first thing that comes to my mind when I hear that a bike needs to be popped in order to start is low compression. You should do a compression test and see what you come up with.
You have to keep in mind that these machines are 25+ years old and most of them need a lot of attention. They can be had for relatively cheap sometimes, but that is because they need a fair amount of TLC. If you're not looking to spend a ton of money than go get yourself a fishing rod or something.
85 Tri-Zinger 60
85 ATC250SX
86 ATC250SX
87 ATC250SX
02 XR650L conversion
84 ATC 480R