You can go about it two ways. You can buy new wheels with a cassette hub, which will have 130mm rear axle spacing. Your bike probably has 126mm rear dropout spacing, but you should measure it to be sure. To flex the stays apart by hand 4mm when you install the rear wheel is very do-able, or you can cold set the frame, see Sheldon's site for instructions. With the new cassette hub, you can use a 7(with a spacer), 8,9,or 10 speed cassette. The nine speed chains are narrower, the ten speed chains narrower still. Your derailleurs will probably work whichever you choose, but you'll have to try it to make sure. And I'm less sure about ten speed items being compatible with the older stuff than the others, I've never used ten speed stuff myself. Shop for some Mavic Open Pro's laced to 105 or Ultegra hubs, probably a little over your budget, but a great value. They'll probably be machine-built, so be prepared to check the tension, trueness, dish, etc. right out of the box.
Since you say you can build wheels yourself, the other option is to stay with your freewheel hub and just re-lace the hub to some newer rims. Mavic Open Pro's and double butted spokes would be nice.
One other thing that needs to be asked: are the current rims 700c, and not 27?" If 27", you also need to make sure you can adjust the brakes downward in the adjustment slots at least 4mm to accomodate the slightly smaller (8mm less diameter) 700c rims. If brake reach turns out to be a problem, you'll also need to solve that issue when you make the switch to 700c rims-