I use FireFox and Chrome and don't have any problem with either of them.
In terms of SWC gameplay, both are pretty equal.
But if you're going to be clicking on CP banners and visiting gaming links, which have a much higher likelihood of containing malicious content, I suggest Chrome. There are just fewer exploits for Chrome, therefore you're statistically safer.
I am forced to use an older IE version at work online, so if I log into SWC from work, there are some minor, but glaring things that just don't work on IE well at all....
the hover-over things for scanners and room maps are just not useful or error prone, some selection tools don't work well (like trying to select in inventory by tag), the build request page is a nightmare... etc.
I'ver learned to not do that stuff form my computer and get on my phone instead to do those things... but yeah in summary my older IE version is less than ideal for SWC...
Lahasa: The point of FF portable, is that it'll run off a USB stick without needing to be installed or anything - nor does it require any special privs beyond starting a program, that makes no changes to the computer.