I've been using Mozilla (the current incarnation) for a few years now on win32 (I'm currently using 1.2.1, it's been a long time since I used IE for anything other than Windows Update). It does use quite a bit of memory when it's running, and CPU can jump a bit with certain operations, but I now use it for mail as well, instead of Eudora 5.1.
If anyone's interested, I've written two pages on my site in (the 'mikes' section) about my opinion on Mozilla. But I'd recommend trying 1.2.1 if you're running Windows, and a spec PC that isn't severely (eg. Pentium 1) ancient :-)
I wouldn't download Netscape 6/7, even though they are based on Mozilla, they have these stupid add-ons by AOL which are just nasty. I like Mozilla though.