Reduce Steam installation folder size
Solution 1:
You can delete the appcache folder every so often. This just contains data which is cached, it does however get re-downloaded when you restart steam, but the folder size is no where near as big. I freed up 200MBs by doing so, then the next time I launched steam, it became 1MB.
Another option is to right click the steam folder, click on the "Advanced" button and compress the contents of the folder and sub-folders.
Like sn0w had said, you should also delete redist files if you don't need them.
Solution 2:
You can reset steam installation as explained here: https://support.steampowered.com/kb_article.php?ref=3134-TIAL-4638
Or use Tools like CCleaner (with CCEnhancer) or TikiOne Steam Cleaner as described here.
Solution 3:
I haven't personally tried this with Steam, but I've used it for "moving" big files off my primary SSD to a big secondary drive.
You should be able to create a symbolic link. That will let you store the Steam folders on another hard drive while making it appear as if folder is where it needs to be for Steam. This gives you the best of both worlds. Steam thinks your files are where it wants, and you don't have those big files taking up excessive space on your 120 GB SSD.
For a little more information you can check out this answer on SuperUser.SE.
Solution 4:
In addition to deleting your appcache folder, you can try a few other things.
One is running steam://flushconfig
as described in this Steam knowledgebase article. If there's any cruft lying around in your steam install, this ought to clean it up.
You mentioned screenshots - they are indeed stored in a subfolder of the Steam install folder, specifically in something like:
C:\Program Files (x86)\Steam\userdata\<your user id>\760\remote\<game id>\screenshots
There may be many, many megabytes worth of stuff in here, depending on how frequently you take screenshots. You can safely clean out whatever from this directory, and you could always symlink this directory to some other bulk storage drive if you want.
Finally, my go-to solution for finding large folders and files under Windows is WinDirStat. Point this at your SSD, and it will show you were all the large files are lurking. You can also drill down to your Steam folder and see what folders/files are taking up most of the room.