I have a beige 2000 myself that I purchased with 36k miles on it. My car wasn't loud at all at first, but once I replaced the intake it had a mighty growl to it. Check to see if the previous owner removed the resonator (inside the front left fender well). Sometimes people remove it for the sound.
I would have to say the main "concern" for this gen neon would be the dreaded "cold-start-knock". I started getting a slight knock around 42k miles, in the morning when the engine was cold. It went away after the engine warmed up. This is an inherent problem on the Neon due to unusual piston wall gap. And yes, the idle is quite rough, also a perk of driving the Neon =). I don't want to recommend ripping stuff out and replacing it cuz I don't know what's up with your car, but the rough idle could just be the 'normal' Neon thing.
You will get 100 different answers on what tires to get =) It depends on what you want. My car is a daily driver but I like having good performance. I went with Dunlop GT Qualifier 205/50/15's, an all season performance tire. The price was great, the treadwear is good, and the wider/lower profile is sportier than the 185/65 Eagle LS's that came stock.
Hope some of this helps...
