(I’m currently writing this using Tor Browser, my “everyday” browser)
It is not my experience that Tor is slow. I am one of the most impatient people on the planet (you should hear me yelling at computers that use Windows) and Tor is perfectly fine for me. Tor should not be used for torrenting, and large file downloads may take a while, but for day-to-day activities, Tor is perfectly usable. There are certain sites where you shouldn’t use Tor but not because Tor is not secure–it is because those sites block Tor or will lock accounts trying to be accessed from Tor because the traffic is labeled as “suspicious” (banks do this).
You can go ahead and do all the browsing you want, including using those accounts tied to you:
There’s generally nothing wrong with logging in to “real” accounts over Tor.
Tor Browser intelligently isolates your traffic so logging in to your “real” Facebook while doing secret stuff on a different website is not correlate-able via traffic patterns.
It also isolates local state (like cookies) so it won’t leak that way.
That excerpt is from a piece on Matt Traudt’s blog, which I highly recommend reading, (and here is the v3 onion link for those interested that already use Tor).