Originally Posted by FBinNY

IME - it rarely makes sense to rebuild a rim onto a new hub. The cost will likely be higher than a new wheel, and you'll have a used rim in the bargain.

So, shop wheels, keeping in mind that what matters is the right axle width and number of speeds and cassette compatibility, ie. any 10s Shimano (type) rear with a 135mm axle can be replaced with any other.

You may opt to match the rim for cosmetic reasons, but it's not necessary, though you'll want to stay close on width. All other things being equal, stainless DB spokes are preferable and worth the cost differential.

However, before you cross the new wheel bridge, take the old one to another shop. It's not rare that one shop will succeed where another failed.