I assume the files you cleared today were in your Downloads folder? If so, that's OK. When Custom Content are installed, your computer takes the most important information and stores it away in the DCCache folder, which is why we always say never to empty that.
I would recommend a reinstall in this case, however, you could narrow your problem down before you do so by doing a "Factory Reset". This is when you rename your "The Sims 3" folder to something else - I usually categorize mine, so I have "The Sims 3 - Dynasty" (some shiny CC is installed, graphics settings are a mix of beauty and performance, windowed mode, absolutely no Mods) "The Sims 3 - Casual" (where anything goes, I have several Mods installed there) and "The Sims 3 - Challenges" (graphics settings lowest for optimum performance, no CC, no Mods, no additional content beyond EP's and SP's). Rename it to "The Sims 3 - Probation". Launch the game, and try to play.
If you succeed in playing for a good deal of time, slowly and steadily add in your content. I'd start with any CC - Store Content, patterns, dresses, etc - then Saves, then anything else you need. Add in two or so items at a time, then play the game. If your game starts crashing, then whatever you've just added obviously is causing the crash, and you can narrow it down further by adding in 50% of the content. I'm not really very good at explaining it, so you can look at SimsWiki's
50% method. It says Mods, but you can apply it to anything - Saves, CC, whatever.
If the crashing still persists in a new, reset game, then the problem is most likely in your Program Files folders, and that's not as easy to fix. You'll probably need to reinstall your game, and I would recommend installing it in this order:
TS3
Patch TS3
WA
Patch WA
Ambitions
Patch Ambitions
LN
Patch LN
OLS
Patch OLS
GEN
(EA stopped releasing individual patches here)
PETS
KPST
SN
Seasons
If this does not fix your issue, you most likely have an insufficient graphics card. Do you play on a Laptop or a Desktop? Do you know anybody who could tell us if your graphics chipset is integrated or not? (If you can't tell us, don't worry.
) What I would recommend before you purchase anything, or update anything, is to take a look at the
Crash Log Analyzer. It can try to tell you what's wrong with your game.
To answer your question about transferring your game, you simply need to move your "The Sims 3" folder to the Desktop, uninstall, reinstall, and place your "The Sims 3" folder back in "Electronic Arts" folder.
About Mods. Yes, most Mods that do this are safe. I'm not saying they all are - while you can be almost certain that Mods at larger sites (MTS, etc) are safe*, there are always those who intentionally sabotage their Mods to do unsavory things. That's why I almost always exclusively download from Creators I trust, or large Sites. For instance, I will only download Leefish's items, NRaas Mods, MTS items, NonaMena's things, etc. If I download from a lesser known person or source, I will always do my research first.
I wouldn't say "Go to Mods" as a first resort. Try everything I've mentioned and if nothing else works, go and download Overwatch, ErrorTrap and Saver, all made by twallan, who is pretty much the King of Modding. The former can really help to make your game run smoother, ErrorTrap
should stop crashing (or at least generate helpful logs that twallan can debug) and the latter will let you regularly save your game so if the game does crash, not all is lost.
*MTS Mods are safe because their upload process is very comprehensive. For instance, a specialized Moderator approves uploads - so someone who has zero experience in Script Modding will never approve a Script Mod. I've uploaded one item and it took about three days to be approved, as I had to add in compatibility information, what my Mod overrode, and go into detail more (I think).