Buying a used 2001 GS500 as my starter bike

[mr72]

well you may be stalling it by braking without first pulling the clutch (I know, dumb question, but you never know). "jerking" and then "just stops" when you come to a stop sounds a whole lot like stopping in gear without pulling the clutch lever.

If you are coming to a stop with the clutch pulled all the way to the bar and it "jerks" and "stalls" then I can't figure what would cause it to "jerk"... I mean, it should basically coast smoothly. The engine may run rough and stall, which probably means the pilot jet is clogged in each of the carbs. Remember, you are going to have to go through these carbs and clean them thoroughly, probably replace those tiny pilot jets because there's no way to know they are not clogged unless you have a set of precision drills, and replace all of the o-rings, especially the pilot needle o-ring. Until you do that, bet on it running weird.

FWIW my dad has a '07 or so Honda Shadow 750DC and he bought it with about 2500 miles on it, had the carbs "professionally" cleaned when he got it because it ran poorly about 4 years ago. It did fine until just recently when we noticed it was leaking fuel from the carbs somewhere a few weeks ago. Now it has about 8K and we had to pull the carbs and completely go through them. This time I replaced all o-rings, gaskets, float needle valves, and thoroughly cleaned and re-adjusted things. 5K miles with ethanol gas will do a serious number on motorcycle carburetors. Runs like a champ now but it is a constant effort with carburetors.

[Watcher]

You should consider professional training, like an MSF course.

It will really help you learn to operate the machine properly, will.give you a lot more confidence, and may rule out you as the culprit with some minor issues with the bike.

[Bluesmudge]

If it has 12k miles on it and has never had the valves adjusted, the valves might be too tight. Especially if the symptoms you describe go away after the bike has been running for 10 - 15 minutes. Or maybe the clutch cable isn't adjust properly. With the bike off and in gear, does it roll around almost as easy as neutral when you pull in the clutch? When you are sitting with the bike on in first gear, does it seem like its trying to inch forward even when the clutch is in?
Of course, first rule yourself out as mr72 has described. I agree with Watcher, if you haven't taken an MSF course to get your motorcycle endorsement you need to do that.