I'd like to try some games.ABSOLUTE noob.

[Violet]

So you need games that are easy for a nongamer to pick up, playable with low APM, and which are cheap/free and for the computer.

Immediately what comes to mind is varieties of Tower-Defense games. These games are strategical and often easy to learn. Don't become upset if you lose a game like this... one can play these games for years and still find them a challenge.

I believe Plants vs Zombies is the best introduction to the genre.

http://www.popcap.com/games/plants-vs-zombies/online

Intermediate: these games hold your hand a little, but the basic formula from beginner games is all the same.

http://armorgames.com/play/522/antbuster

http://ninjakiwi.com/Games/Tower-Defense...fense.html

http://gamejolt.com/online/games/strateg...ense/2369/

Advanced: If you become familiar with the genre, you might well appreciate such games as these:

http://www.candystand.com/play/vector-td

http://www.gemtowerdefense.com/

http://www.flasharcade.com/tower-defence...fence.html

Note: this is not the only type of free game... but these are games that will certainly run on your system, and you might enjoy them.