I use Firefox 2 here regularly, with a dialup connection yet, and hardly ever have any trouble.

I have Firefox 3 on my "spare" computer. When I tried it out for a few days, it seemed to work no worse than Firefox 2.

Years ago I used to have a utility called Net Medic, now obsolete, that would hook into my browser and keep track of the data traffic: how fast the reception and transmission were, how many "hops" across the Internet it took to reach a given website, and where any delays seemed to be located. I haven't checked to see whether there are any up-to-date replacements for it. If they exist (and aren't outrageously expensive), something like that might help you figure out what's going on with your system.

I think two of the reasons the original Net Medic no longer works are that (a.) it was only designed to hook into certain old browsers, none of which I'd care to use any more; and (b.) it relied partly on something like identifying and "pinging" individual routers along the way to see how long it took each one to answer. Those routers were reprogrammed years ago not to respond to such pings any more. Any replacement for Net Medic would have to deal with both of those issues.