To make it a little easier, since your comp only has 64Mb of RAM the changes of running a live CD or even a GUI is small. Your best bets would be to try Puppy (which you have) or possibly Arch Linux. You can attempt to install Slackware, but if Arch doesn't work then Slackware won't either.

The only other option is for you to install a distro that has no window manager and runs in Command Line Mode, which means that you can't use apps like firefox or anything Graphical User Interface based. But in CLI mode you can use links or lynx to access the internet in a text based browser.

I think you have confused terms, windows uses a paging file, in Linux you setup a swap partition.

The general recommendation for a swap partition is to make it 2X the amount of RAM installed, however with your current amount of memory I would recommend setting up a 2G swap partition.

Swap can be a file, but usually it is setup as a partition. Swap is a location on a hard drive that is designated for less used memory files and is also used as RAM if your used memory exceeds your physical RAM size.

You must remember that your hard drives are much slower than RAM chips, even though with swap you may be able to run many things, the performance will be highly degraded compared to running the same apps from RAM.