02 250 starts and then sputters out

[Demon49]

I'll get one of those tachs asap and check. I've drained the tank with the petcock set to "prime" and it flowed great. It did have a slight kink in the fuel line coming from petcock to fuel filter, I got it out and replaced the line. The fuel filter looks good, but I guess that doesn't really mean much. Do I really need a fuel filter? It didn't come factory with one did it? I'll try draining the carb before I ride and after it cuts off and see if it's the same amount. My choke won't stay in the "on" position by itself, I have to hold it the whole time. Is that a problem? I've tried removing the gas cap and riding and it does nothing, it still dies. I'm gonna go ahead and rebuild the petcock just in case. How long does it take generally for a 02 gz250 to warm up? I'll check the bikes coil before ride and after but I don't know if it's getting to full temp in that short time. Would that matter? Thanks you all very much for your advice!!!