First, a link for Debian Based Distributions suitable for old computers.
Desktop: The GUI will take up quite some of your resources in RAM. The Window Managers I got lucky with while working on an old machine and a Netbook are XFCE, prefering LXDE and am currently very happy with Openbox.
Suggestions: I would suggest to get a live image of Crunchbang Linux and give it a try. If so, I would recommend using Crunchbang 10 [Statler], based upon Debian 6.0 Stable [instead of 11 – which is based upon the 'testing' branch of Debian].
As Debian runs like a charm on my old machine, it doesn't run as nicely on my Netbook. I was quite lucky with Linux Mint Debian Edition until I found Crunchbang, which is the closest to Debian that is currently possible for me here. When working on the command line, reading documents or comparable low-resource applications the CPU is up to about 5 to 10%.
Using a lightweight browser like Midori instead of Firefox saves also loads of resources.
Games: For games mainly known to run on Windows [Worms Armageddon, Diabolo 2] you'll need something like WINE, yes. And yes, you'll need Windows available somehwere on your machine [this is how far I understood it].
Recommending to use a Virtual Machine with just 64 MB RAM would be a bad joke, I guess.
Damn Small Linux: There was little to no progress for a very long time [years?] on DSL, but the project was resurrected at the end of 2012 by the main supporter! So as I didn't tried it out myself so far, this is one distribution worth a look for using with limited resources.