Originally Posted by Antipodes

Yes, stripping and rebuilding whatever possible is a good idea. Going on what seems like your limited understanding of bicycle mechanics, you can either opt to do the work yourself (which requires a lot of specific tools and a bit of prior studying/reading), or take it to a local, reputable, bike shop to have the work done for you.
The best thing for the bike is an overhaul - clean, inspect and grease all bearing surfaces (bottom bracket, headset, both hubs), and make correct load adjustments. Inspect cable housing for cracks and breaks, and replace with new housing and cables if necessary. Inspect tyres for cracking and dry-rotting and if absolutely necessary, replace. The list can go on - depends on how much you are willing to put in, and more to the point, pay, if you have it done for you.
The Campagnolo parts are Triomphe, from the mid '80s. They look okay, but I guarantee that Shimano parts from the same period will perform a lot better, especially when it comes to shifting - derailleurs (especially the rear), shifters being the obvious points. If you want indexed shifting, you are looking at a total makeover to a pretty much all-Shimano drivetrain.
The brakes are good, pretty much like any single pivot sidepull from the period. The difference here comes more from non-aero v.s aero levers, the latter having more mechanical advantage. Yours has the former, but you can easily change if you desire.
It all depends on whether you want fashion or function. Campy parts may look better (some may argue this point when it comes to the Triomphe group), but Shimano will provide for a nicer ride. I'd say keep the Shimano f. derailleur if it's in good shape - make sure the springs still seem strong, there isn't too much play at the pivots and wear on the inside of the cage.
You will not need a new cassette if is it isn't worn out (check for skipping under load, especially whilst running the hardest two or three cogs).
I know this all opens up a can of worms for you, but hopefully it is of some help.