I've got three Dremels at work, and the missus has a hand held jobbie for jewelery making.
I use mine more for cutting plastics and finishing rapid prototype parts, she uses hers for polishing and drilling.
We tend to have the same complaints, you have to take your time or you burn through the accessories, and you end up with a better finish. You'll find an initial glut of spending on things like the larger collets, and variety boxes. These days she tends to buy the cheapo kits from ALDI when they come around and finds identical performance to the Dremel ones, but when in doubt we both revert to B&Q's pretty extensive range of genuine Dremel.
I've bought two Dremels direct from a web based company i can't remember the name of, but the Dremel its self worked out at about £20. Cheaper than repairing a broken one annoyingly. Also, she tend to get miniature drill bits from APTC (Axminster Power Tool Center) in Nuneaton, probably because thats where i send her!