In reply to Martin W:
I've built a wheel, you can do it with a spoke key, a bike frame and nothing else. Thread the nipples onto the spokes to a set point (e.g. to the end of the threads) then wind on a turn or two per spoke and keep going round till the tension comes up. Then you have to true it. But there are a Million online tutorials to follow which are better than my advice. I wouldn't do it again as:
1) It takes ages when you are not used to it
2) I don't think I built a particularly good wheel
3) It made my back ache sitting over an upside down bike
4) In the context of how long it took me I think £25 is cheap to get somebody to do it for you (somebody sitting in front of a truing stand with good ergonomics and probably paid for their time).
To avoid the problem happening again go with a shimano hub, typically cheap and they seal them properly, plus the flanges are wide enough to prevent problems with knacking the J-bend in the spoke. Claris is bottom of the range and supposedly good and rugged. Having said that the Miche and Easton ones I have had have all been good too.
Cup and cone bearings are particularly tolerant of being miss aligned, rusty etc. Cheapest option is to get some very high grit wet and dry and clean up the rust with that.
I am not aware of people replacing the bearing cup/cone but it might be possible, I'm sure its an interference press fit since the hub body is typically aluminum.
What is the rim wear like? You might be wasting money if its worn but I guess the LBS will advise on that. Also you may need new spokes if you change the hub unless you replace like-for-like.
Finally have you considered just buying a new wheel? You can get a full shimano wheelset for about £80.
Post edited at 10:23