Chokes can be adjusted/repaired. Take the air cleaner off and watch the carb as to is running and stall, OBVIOUSLY at idle. You can watch the choke to see if it is staying closed after warm up. I suspect your carb may be loading up due to a float being stuck too high or your needle and seat may be stuck. You may notice while it is running heavy black smoke from the tail pipe, you may actually be able to see fuel dumping heavily into the throttle bore (carb opening) before it dies. As soon as it dies grab the throttle linkage and stroke it while looking down the throttle bore (far enough away so that you don't get any fuel in your eyes or burn your eye braws if it backfires) what you are watching for is fuel squirting into the bore from the accelerator pump, if it squirts you have eliminated a down stream fuel supply problem for the most part. Next I would hold the pedal to the floor and spin it over until it starts, like when one is flooded, watch for heavy smoke out of the tailpipe upon fire up. If so it supports what I suspect about loading up. It sometimes canbe cured by simply tapping the fuel bowl area wear the line comes in with the handle of a screwdriver, hard enough to jar it loose but not hard enough to damage anything (which would be hard with plastic handle screwdriver). If it is predictible I would try this and see if it corrects the trouble if it returns you may need togo in it and clean it out. This can be somewhat of a common problem with vehicles that sit. I have also seen cases although rare, ESPECIALLY if it is pretty much stock, were the fuel pump is creating enough pressure to over power the needle and seat, this situation usually last well beyond normal start up.
Hope this gives you something to work with, if you would report back after you check it. Good luck.
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