What would your mom use it for? If only for particular applications that are definitely on Linux then you could probably set it up for her and she'd only need to patch it once in a while (not as often as Microsoft stuff).
If she expects to buy hardware, games/accounting etc etc software in the local store and use it easily, or swap stuff with other users on Windows/Mac then I'd go for Windows/Mac.
The advantages of Linux IMHO, are stable, rarely needs patching, does more in less memory, hardly any viruses. Disadvantages are lack of consistency across applications, lack of built in help and documentation, sometimes takes a while for new hardware to be supported, harder for beginners to do "simple" stuff, less "how to" books available, may
be harder to connect to your broadband supplier.
Of the commercial Linuxes I like SuSE best. Wouldn't recommend free ones for a non-techy user (assuming she is) because of the hassle of downloading all the right packages; can be a very tedious iterative business. SuSE is a nicely packaged collection of good stuff with a relatively simple install process on standard hardware.
Personally I'd still put anyone non-techy on Windows or Mac (that should be enough to start a platform war