I just purchased a 2009 GEM E4, its pretty ragged out but for a few hundred $ i had to take it, The tires are aired up and it rolls, NO batteries, no charger and the stock motor is in the floorboard. I would like this car to go fast so im prepared to spend some $$ to make it happen, so what is the the BEST motor i can get and what is the best LiOn battery option that wont break the bank? Is the stock controller ok or should i plan on replacing that as well,
Thank you
Congrats on your acquisition, maybe. 
First thing I would do is try to power up with minimal expenses, borrow or charge old batteries, reinstall motor, see what happens.
Once operational, upgrades can be endless and costly. The sky really is the limit.
I did high voltage Volt conversion. Seems to be most cost effective upgrade. Nearly a bolt in conversion. Leaf cells are also popular.
Motors are a different story. Lots of thoughts and opinions. Do your research for what your goals are.
Final drive ratio is final (or first) objective to establish. This is overall tire diameter times ring and pinion ratio. Look for no more than 6000 rpm at chosen cruising speed. Charts are available here and online when searching.
Controllers can be programmed and all kinds of hacks can be done! Just research this forum.
All of that being said (typed) top speed can be upwards of 50 mph!
It is rather thrilling (scary) driving a GEM that fast so be careful of what you wish for!
Have fun and be sure to report back.
Good luck. I’m in the same boat with a 2000 e825.
Once you get it powered up and verify all electronics work as intended get with Inwo here or spec out and install lithium cells. Less voltage sag and way less weight, this is the best performance option and can drive the stock motor just as good as any motor upgrade on deep cycle batteries.
Lithium is slightly more then the first set of deep cycles but depending where your at you won’t need to replace them every couple years so total roi is much better outside of the performance.
M@