I'm riding a Fuji Finest-Al with Bontrager Select Wheels and Look pedals. I know that this is really a beginners bike, but that suits me for now because at 20yr old and a students you'll take what you can get. How far can I take this bike in regards to racing? Can you think of any other upgrades I should look at to lighten up the bike or should i really be looking towards putting my money towards something new in the near future?

Thanks for any and all help!

Go ride some big road climbs and race the heck out of your current bike.
Save your money until you've done many races: then you'll know where to spend the precious dough.
Go do crits, road races and centuries but most of all look, go road ride up big hills or mountains.
Pick up a copy of Bike Racing 101
like some riders in this site have said: do not upgrade, just go [ride] up grade