am I the only one who upgrades parts that are working fine just because I want something that works better? Or looks cooler?

To answer your question, wheels/tires will make the most difference in your ride, but wheels are expensive. Start by getting some nice tires.
As far as drivetrain, if you ride a lot your chain will need to be replaced soonest, followed by cassette and chainrings. As those wear out, upgrade them (though maybe not the chain, most chains are pretty much the same). Your rear mech will probably get killed by a tree at some point, so then upgrade that. Crankset is expensive, but can save a lot of weight, so if you have some extra cash I'd look at upgrading that as well. Stem/handlebar/seatpost change the feel of your ride very little (unless you change angles/widths/etc) so those should be last, IMO, but you CAN save A LOT of weight in these areas so if you are going weight weenie then they should be replaced earlier.

Cheers, and have fun with your new ride. Welcome to the world of the technofile