I know this is probably a noob question, and one that has been beat to death, but I haven't really been convinced.
Is it ok to leave my computer on 24/7? Should it be in sleep mode if I do?
The only thing wrong with keeping it always on is that dust collects, otherwise computers are happiest being left on. However for power reasons I have my laptop set to turn the monitor off after 15 min and go to sleep after 2 hours.
If you plan to leave it on for an extended period of time, you should make sure that your fan intake vents have enough room to get some clean air. You shouldn't leave it flat on a desk at a wall corner, but try to put it in the center of your desk and elevate the back (if the fans are back there). That way, you get some nice clean air running through your computer to keep temperatures down.