As a forum member reaching the ....um shall we we say "silver surfer" end of the spectrum AND a Linux newbie/noob I would say go for one of the newest releases of either Ubuntu, Mint or Fedora just because they are ones that work "straight out of the box"
DL and burn a Live CD iso version of each and boot to them and have a look at each first to get a feel for them
You can dual boot with your current Windows OS so that you have a fall back if you have problems and need to search for a solution via the various forums online. It WILL happen that you run into a small problem or 2.
Alternately, get hold of a cheap smallish second hand HDD and install to this, with your main Windows OS un plugged, and have a go. That way you can make mistakes and not have to worry to much. Don't be afraid to experiment and if required re install and try again.
Lastly research before you start!