These days I would strongly recommend at least a 240GB drive unless your budget is super tight. I've lived with a 60GB SSD for a couple of years, moved to a 120GB, and am now on a 250GB. This is the first time I've gone for an extended period of time without having to clean things up.
A fresh build with a couple of games will fit easily on a 120GB drive, but stuff accumulates and eats into your free space. You'll find that you have to monitor your free space pretty closely and perform pretty regular maintenance to clean up junk. None of that is a major issue, of course, so if you budget is tight that's a perfectly valid solution but...
The issue is that the price difference between 120 & 240/250GB drives now is tiny.
At the budget end an 120GB Adata SP550 is $38, or just $20 more for the 240GB drive.
The 850 EVO is $69 for the 120GB and again, a tiny $22 extra for the 250GB.
For me, I'd happily spend $20-25 to avoid having to muck around with managing space. It's a no-brainer. Though of course, if your budget is super-tight, it's little $20 decisions like this that often end up blowing it completely, so decide what's right for you.
It is worth noting as well that the 250GB drives perform better too as they have extra channels.
RE "what you you store on the SSD", the key thing is your operating system, which is best if you can actually perform a fresh install of your OS on the SSD. There are other options (Google them) if you don't want to do that. Other than that, install programs you use often (Web Browsers, Office Suite, etc) on the SSD, and if you still have space, a key game or two (or however many you can fit) which will save you on load times.
Just remember to keep at least 15% free space. SSDs don't like being full, it massively affects performance and can impact the life of the drive.