Sory to tell you this, but there IS malware with linux.
Your chance of catching something nasty just surfing round the net with a supported linux distro is very low (virtually zero) but malware still exists. The most famous of the linux malware is the december 2009 'waterfall' screensaver.
Almost all linux dsitros need to be installed into one of the linux filesystems, not a windows (NTFS/FAT) filesystem. It is possible to install onto a windows filesystem with ubuntu (and possibly with mint and/or some of the other ubuntu based distros) with 'WUBI'. WUBI isntalls like a windows program rather than the normal way an OS installs. I *think* its possible to install onto an external drive with WUBI, but I'm not sure...I'm not a ubuntu fan really, and WUBI has always seemed like a bit of a dirty hack to me anyway.
If you install with WUBI you shouldnt lose any inormation of that partition.
Be warned, running from an external drive is slower than if you use an internal drive (USB 2.0 HDDs are pretty slow compared to internal)
BTW, its a good idea to use 'storage space' or some similar term when describing your HDD space. Using 'memory' can lead to confusion with the RAM. Also, if you have drive 'H' on your external drive, that is already a partition.
I'd suggest if you do decide to install ubuntu to get kubuntu or xubuntu. The difference between ubuntu and kubuntu/xubuntu is the DE (desktop enviroment, the desktop GUI). Ubuntu 12.04 uses 'unity' as a DE, which IMO is one of the biggest PITA DEs ever made. Kubuntu use KDE, and xubuntu uses Xfce, which IMO are better all round than unity.
You can try ubuntu, kubutu or xubuntu from a liveCD (just burn the .iso you download to a CD). Or, if your system doesnt have a CD/DVD drive, you can put the .iso onto a USB stick. Running as a liveCD or liveUSB will not change any files on your system, so you can try out the different versions or other distros without installing anything. Running from a liveCD/liveUSB will be slower than if it was installed though.