I'm using a WRT54G (with firmware from Sourceforge) and a built-in Broadcom a/b/g adapter. Also have 2 other laptops here using Linksys B adapters, and one desktop on a wired adapter. All are rock solid all the time.
I have no experience with USB wireless adapters, but I know that the Windows Wireless Zero service is apparently giving wireless users problems. Try disabling that once you have your connection set up (which you already do).
Also, if you are having problems with your router, I would personally try going back to the stock Linksys firmware. Sveasoft, even though it's not free, is still a hacked firmware and who knows if it is really compatible with all the adapter types out there? It's easy to reinstall if it doesn't help your problem, and it's a good place to start.
This is my third Linksys router, all of which have been replaced for want of new features, not because of any problems with them. My first Linksys router, at least 5 years old now, is currently running in somebody else's network without a hitch. I would definitely buy another Linksys router if I had need of one.