My suggestion would be to visit your local sewing machine store, if you can find one (they usually also sell vacuum cleaners), and talk to the salespeople there about your needs. You might be able to find a higher end used machine that will work on the fabrics that you mentioned. The brands that have a good track record are: Pfaff (I have a 7510), Viking, Bernina, and Elna. If you find a reputable store that will provide a 1-3 year warranty, I think you will be happier in the long run. They also usually provide classes as well.
In my experience, the Brother and Singer brands are not terribly reliable. The Singer 7422 has some negative reviews that I would be concerned about. The 7470 sounds a bit better (check out the reviews on Amazon).
If you have any other questions, let me know.
Good luck!