My first guess is that the idle circuits in your carbs are clogged from sitting, and the previous owner missed curing that when he cleaned them.
Could your transmission trouble be related to the feature of this transmission that helps you find neutral? When the bike is stopped, you can go from neutral to 1st and back to neutral, but not past neutral to 2nd until the engine is running and you're moving. You should be able to get it into neutral by moving the bike back and forth a little though. From 1st gear, lift the shift lever up all the way firmly, which would get you into 2nd on most bikes, and it should go into neutral.
Welcome to the board, Jon!
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