Late 2013 21.5" iMac, 8 GB Ram, 1TB HDD. After update to Catalina 10.15.1, the thing was turning into a brick. Nothing worked, Office 365 took 3-4 attempts to launch and only did so after 10 minutes. Chrome, Firefox, Safari were crashing continuously. Creative Cloud, Photoshop, Lightroom, a nightmare. Performance was slow and buggy across the board. Wanted to throw the thing out of the window but, being stubborn, decided that no machine and some crappy software were going to beat me. The age of Terminator ain't not quite here yet. Started in Safe Mode, suddenly everything worked, like a gazelle compared to a Soviet agricultural tractor of the 1950s. It wasn't a matter of CPU or Memory usage, which were all well within the green. Here's what worked for me:
In System Preferences:
Turned off Siri, since I don't use it.
Turned off font smoothing and dynamic desktop.
Removed most of the extensions that I wasn't using anyway, almost 90% of them.
Turned off Notifications for all the things that I didn't care to know about in real time.
Made sure that there were no unneeded Login Items under the User and Group preferences (which in my case were none).
Changed the DNS servers in my WiFi connection to Cloudflare's faster ones (184.108.40.206, 220.127.116.11 and their IPv6 equivalents).
This improved things somewhat, but it was still not performing as expected.
Removed all the Adobe and Creative Cloud processes that were running in the background and prevented them from launching at login in the first place by deleting all Adobe launchers in HD/Library/LaunchDaemons, HD/Library/LaunchAgents and usr/Library/LaunchAgents. That did it. Restart, and suddenly everything worked. The Verifying App dialog now takes 2-3 minutes instead of an hour, Office 365 launches in 20 seconds, all three browsers launch in seconds as well. Adobe apparently is not yet fully compatible with Catalina and just messes everything up in the background. Will use GIMP for the time being. If I have to use Photoshop or Lightroom for some reason, will have to do a quick file cleanup afterwards - like cleaning up after your dog. Now the birds are out, the sun shines, and I feel like a better human being. Hope this helps!