If you've just got a few broken spokes, you should be able to fix the wheel without too many problems. Whenever you lose spokes, the wheel will always warp and go off-center.
A few new spokes and a little truing and you should be able to pull the wheel straight again. It's relatively easy to straighten out even 1 or 2 inches of warpage, unless you've got a really bad dent. Alloy rims are easier to straighten than steel rims.
If you take it to a shop, they should only have to charge you about 50 cents/spoke for your broken spokes (plus maybe a few extra), plus about 1/2 hour of labor. There should be no need to rebuild the entire wheel.
If you've really got irreparable damage on an inexpensive bike, it would probably be cheaper to buy a replacement wheel than try to rebuild your existing wheel.