If you want an living room PC for entertainment, Windows is king. Neither Linux or OSX support Bluray properly and Windows still has a huge edge in gaming. Windows also supports the most hardware. That's become unimportant to most people, but if you work in a research lab with various oddball computer controlled devices around, you are often forced to work with Windows simply because that's the only OS supported by drivers for a lot of things.
OSX is the perfect OS for your mother. There's the one "Apple way" of doing things, so if she needs help it's easy to give her some. OSX gets decent battery life (on mac hardware) and still has a few Unix friendly features that haven't been locked away by Apple yet. If you're looking for a ghetto linux workstation, OSX will do in a pinch. I actually spent the better part of last year working under OSX on a Mac Book air. I've used Mac's off and on for decades and this is just the most recent stint (The MBA hardware lured me in this time). It worked, but the OS still puts up too much fight you when you try to customize it. OSX has also gotten rather buggy. I'm relieved to have retired it. As I said, while it would be great for my mother I personally detest OSX. Also, Mac hardware is moving away from the DIY crowd. e.g. The MBA's actually use proprietary screws to keep you out of your own laptop's innards. If you've ever saved a laptop from a coffee spill by disconnecting the battery and opening it up and doing a little cleaning, just bear in mind you won't be able to do that with most future macs.
Linux is bug central. Don't get me wrong, it's come a long way from the days when Slackware was king. You can install Ubuntu and almost everything will just work. The devil is in the details though, and if you have a low tolerance for flakiness you'll have to tweak away. However, no other OS is as powerful and flexible. If you want it to do X, it can do X in dozens of different ways. If the journey is as important as the destination for you, Linux is your OS.
Windows is all things to all people, but entertainment first and foremost. OSX is for your mother or people who would rather not use a real computer. Linux is for those who embrace the quest. Decide (and be honest with yourself) what kind of user you are and your OS preference will become clear, although what you are forced to use may be different. I currently use both Windows and Linux extensively, and occasionally help my Mom with OSX.