I agree with
freeranger to start with tires, tubes, and brake pads. You'll see the biggest differences from these and they'll get you going and then you can figure out what else you might want to do.
For tires, I'd recommend the
Continental Speed Rides (out of stock at that website, but perhaps your local bike shop can get their hands on some) They're light, comfortable to ride, and inexpensive -- a great value for what you pay (which is usually about 25 dollars each). They're way better than any Bell or Innova brand folded tire you might find at Walmart or Target.
Tubes are pretty standardized and you can get these anywhere. I prefer the
Continental Conti Tour tubes, as they have a threaded Schrader valve with a little nut that helps retain the valve stem during air pressure checks or inflation.
For brake pads, I'd recommend either these
Kool-Stop dual compound pads or these
Jagwire pads. I have used both and have been pleased with both.