You'd be right in thinking that you need a swap partition, and it's wise to have a home and root partition.
This guide might be of help to you
It's quite basic, but it runs you through what you have to do, and how it does it, and explains it better than I could.
The reason it is not being displayed in its full resolution is that it is not using any graphics accelerators, only the ones it has on the live cd (if any--I'm not an expert in these things), but once you have installed you can run the program 'envy' and choose to install the latest nvidia/ati drivers. I have had some issues, but look through my posts to see how I fixed them (my most common fix is here. http://forum.linuxmint.com/viewtopic.php?t=2970
If this doesn't work, then just post your xorg.conf in the forums and people will help you out
IN the install, it should sort out all your network stuff for you (it does for me, using an onboard controller.
I hope that helps, and I hope that eventually you decide to drop windows! (unless of course you need it for work......)