One of my friends suggest the following.
1) Install a second internal harddrive.
2) Install Linux Mint or Ubuntu in that harddrive.
3) Install FF (or Chrome or Opera).
4) No need for anti-virus.
He said that I could partition the existing harrddrive but might be better to install a second one, so the existing one for Windows and a separate new one for Linux.
A second drive isn't a bad option. Especially if you're not experienced with partitioning drives.
Personally, I don't use any of those browsers, but I'm a Debian / KDE guy. A few things to keep in mind:
1) A big distro (Ubuntu, Debian, Kubuntu, Mint, Open Suse, Fedora, etc.) means choice. If you don't like your desktop, and can't modify it, change it. The same goes for your web browser. Space is dirt cheap, so there's no reason not to have more than one of everything if you want to.
2) Always use you distribution's package / software manager (if you aren't a developer). Always. Never just download some mystery binary. Package management is your friend.
3) Always do your updates. Always.
4) ClamAV, and it's various front ends are free for linux. There are also programs like rkhunter that hunt for rootkits. You should probably still have both, and should run them periodically if you don't run them as system services. You might even consider a firewall, if you don't really know what services you have running. Linux boxes are often attacked because they look like servers. While a given virus might not infect you that can still be passed on to others. Linux isn't magic. It just tends to be more secure by design for all of the software / packages available for a given distribution, and the target of fewer consumer oriented viruses.
As far as your initial Firefox crash goes: 'That ain't right'. It could have been crashing for any number of reasons. FOR ANY LINUX DISTRIBUTION, THE SOLUTION IS ALMOST NEVER RE-INSTALL EVERYTHING. In the case of a program like Firefox, I'd have suggested running it from a terminal / console, and seeing what the program had to say before it crashed. Try looking that up on google. Sometimes it just comes down to waiting for a newer, or switching back to an older, version of the package.
I've had systems with broken kernels, broken bootloaders, and broken init sequences, all mostly self inflicted, and all nasty, hard, problems, that I've managed to fix without re-installing. chroot and a bootable linux on a usb key are your friends.