This is a rather old post, but given that you've not received any answers yet, I hope replying isn't too inappropriate.
For the first question, I back up my files on a NAS using rsync. It's a command-line solution, but I stored the command in a .desktop file to make an icon in my app list that I can just click to back everything up to the correct places. Makes it easy, and wasn't too difficult to implement.
Your second question might depend on your hardware. I just set up a new laptop on linux mint and had to do significant amounts of troubleshooting, all of it involving the command line, because linux mint didn't come with or know about most of the drivers required. If you're using an older or more well-supported computer, it might work better out of the box. Most troubleshooting will probably be command-line, but there's a lot of support out there for that if you need it.
App-wise linux mint has a fairly robust software manager (app store) with a wide variety of apps on it that, for the most part, don't require a lot of troubleshooting. (I only recently switched over to mint from Ubuntu, and was impressed at how many apps you could access so easily, including a large variety of unofficial releases of software that isn't officially available on linux). Unless you're intent on building obscure software from source, installing and using applications should be fairly painless.
I can't speak to the stability of mint, since I haven't been using it for long enough. However, I used Ubuntu for five or six years and never had to reinstall it, so you could always look into Ubuntu if stability is important to you.
AlteredStateBlob