Still a couple of points to the OP, not directly related to what OS/Linux distro to choose, but what kind of issues you'll probably face if you go with Linux.
The situation you have is pretty much the reason I use Linux at home, ie. some old PC where I don't feel like buying/paying for Windows 7, XP (or 2000) is probably too insecure already, and "unofficial" versions of Windowses are out of question of course, because how do you know they are not full of trojans, keyloggers etc. by the happy pirates? (I use Linux also at work, but that's beside the point.). For new PCs which come pre-installed with e.g. Win7, for a home user who doesn't need Linux for studies or work there is very little, if any, reason to install Linux beside it, let alone replace it.
Anyway, the most prevalent issues I fought with Linux (Fedora or Ubuntu) in home use were (I think I've mentioned these here before):
1) Getting my network banking to work. My bank's system was very finicky about the Java version, ie. they required a recent, official Sun (or Oracle, nowadays?) Java client. The OpenJava or whatever that came with Fedora by default wasn't enough, even though it seems to work 95% of the time for any web pages which need Java.
Replacing OpenJava with Sun Java was a bit hard for me, but there were detailed instructions online, even for Fedora (I just Googled +fedora +my_bank_name, and presto, got the instructions, also learned there it was due to OpenJava (Or more precisely, the bank system was stupid for being so finicky). You just had to be very careful that you gave the commands exactly, and it was a bit of PITA. I don't know how many web pages really need the official Sun Java, but my bank did.
2) Watching some streaming videos on some web pages. For some of them, which didn't work right away, it seemed easy to find instructions how to make them work. But some DRM-protected media doesn't seem to be doable on Linux at the moment, mainly the DRM content using MS proprietary Silverlight. There is a Linux version of it, Moonlight, but it doesn't seem to work with some DRM-content, at least not yet. Installing Moonlight plugin was quite easy and semi-automatic, just like installing plugins in Windows (ie. a web page requested for it and pointed me to Moonlight, etc.).
3) Of course I needed to install also Flash Player plugin in order to see Youtubes etc., but frankly I think it wasn't any harder than installing Flash Player plugin on Windows. Adobe has apparently stated that they will not be releasing new Flash Player versions for Linux after certain version, but as far as I understand, it will still be available with Google Chrome browser, and I don't know if it really matters in the long run anyway, if HTML5 etc. will make Flash Player obsolete anyway. IPads and IPhones seem to be fine without Adobe Flashplayer, and apparently Windows 8 Metro will not support it either. Becoming obsolete, it is...
So depending what your home Linux system would be used for, you may run into many compatibility issues and have to google for more information to solve them (and some of them might not be solvable). But overall, I wouldn't fret about it too much, at least for me finding the instructions and answers with google was always quite easy.
Remember that most Linux instructions you'll find will use command prompt, ie. give exact Linux messages you must give in a terminal window. The same can usually be achieved by using graphical user interface (just like doing in Windows), but the reason the instructions online prefer using command prompt is because it is much easier to explain what exact commands to give, instead of "go to this menu, press this button..." etc., especially because the GUI may be different depending which distro, release or GUI you use. So don't be afraid of the command prompt examples.