There is a single upgrade you'll want to do: get some slick tires to put on there. You don't need the knobbies and they slow you waaaay down. It'll cost about $30 for a pair. I like the Bontrager Road Warriors. Nashbar or Performance makes a good cheap one, too.

Aside from that, don't bother upgrading it. You'll wind up replacing every single part on it (including the frame) before it becomes good, and you'll have spent a lot more than a new bike would have cost, particularly if you get one used.

Alternately, keep an eye out for junk bikes with parts you can swap out that will do what you want. A low-value bike is a great way to learn about working on bikes.

Like, a steel threadless fork will weigh less than that shock, which probably isn't that good anyway, and you find them all over the place.