Welcome to the wonderful world of free software, and to these forums (I am new here too, second post).
For what distro you should use, I would say there is little doubt you should use Ubnutu. Apt, the pakage management system used by Ubuntu and all other Debian based distros, is great, and its 12-month release schedule means you always have cutting edge software (there are long-term releases if you don't want to deal with that).
You may want to give Kubuntu a chance (that is Ubuntu with KDE instead of Gnome. Different desktop environment. It will look and feel much different, most people say KDE is more like Windows, and Gnome more like Mac in a way they cannot even explain). You should be able to decide between those just by booting off the live cd and poking around a little.
You mentioned Avast in your software section. You really do not need that. There [I]are[I] no viruses for Linux. If you feel the need to make sure you are not passing on virus to Windoze users, I would recommend using ClamAV. It is open source, so you can install it via apt. Perhaps it is just me, but I find it annoying to have software that I installed through other means, as you then have to update it individually.
For gaming, things get a little more annoying. You will really want to just dual-boot to play many games. Wine is a pain, if it works at all. It doesn't take long to dual boot, and it is not as bad as it would seem.
There are also some good games with Linux clients, such as Enemy Territory: Quake Wars.
So, to stop ranting and actually answer your question, here is what I recommend you do:
Download a copy of Ubuntu, and possibly Kubuntu as well if you have time to fool around. Pick the one you like best.
Install it (it is easy), but set it up to dual-boot with Windows (once again, it is easy. You will have no trouble).
If any of your games have Linux clients, grab 'em. For the rest, reboot. It is worth it.
Just a few random tips:
Don't be discouraged by the ugliness of Ubuntu. It can be easily fixed in the appearance preferences (for more options head to http://gnome-look.com ).
The best way for newbies to install software is by going to applications-add/remove. It is dead simple. Try to avoid downloading software from websites, it should almost never be necessary.