Something that slipped my mind when I was writing that thesis up there.
The replacement router firmware I use is
DD-WRT and the one major thing it did without me touching a thing was make my Linksys router a lot more stable. I torrent a lot and while I was using the original firmware I had to reset the thing at least once every few days. I eventually had it set to automatically reboot itself at like 4AM every day. With the DD-WRT firmware, I regularly have uptimes of months, and never have to reset anything.
Something a bit simpler, which I hear very good things about is
Tomato. 85% of DD-WRT's massive featureset is gone here, but since even a certified network technician like myself doesn't use the majority of those features (But I like having them... ya know.. just in case) it's still a big improvement and people say it still provides that hardened stability.
Full disclosure though, my router is several years old. It's beloved by netgeeks like myself (Linksys WRT54G v3. Cisco doesn't make em like this anymore, hence my bitching above). There's a chance that lower end Linksys routers with their stock firmware don't have those same stability issues under load that they used to. I did look around, but I can't seem to find a solid word that way so I don't know.
Sorry if I'm providing too much info too obtusely, generally when I offer this sort of help I'm right there with the person and I do all the setup myself. I always go with a Linksys WRT54GL and put DD-WRT on it, because it makes me more comfortable and I feel that way there's a better chance whoever I'm helping won't have an issue later since I never do and I don't ever see the settings page unless I intentionally want to play with something, so I know they don't need to deal with it.
I just don't want to force you down a path here, considering limited budget and the ease that talking like this overwhelms most people.