Firefox needs very little to run. Probably less than IE when you get down to it.
You shouldn't have any problems running it on your system. Just be sure to check out the life changing AdBlock extension: http://adblock.mozdev.org
I was considering running Firefox (I think thats what its called) but wanted to see if you thought I had enough "stuff" to run it. I can bring resources up a bit by cutting some stuff out of Startup.
Microsoft Windows 98 4.10.2222 A
Upgrade using OEM CD /SrcDir=F:\WIN98 /IQ /U:xxxxxxxxxxxxxxxxx
IE 5 6.0.2800.1106
On "COMPUTER" as "default"
Compaq Computer Corporation
AuthenticAMD AMD-K6(tm) 3D processor
76% system resources free
Windows-managed swap file on drive C (9807MB free)
Available space on drive C: 9807MB of 11446MB (FAT32)
Available space on drive D: 2207MB of 2858MB (FAT32)