Just upgraded to Catalina and trying to do anything on the iMac takes forever and I get a constant color wheel. I have called Apple several times and nothing seems to help.
Thank you Rod!
Macintosh Beachballs!
Macintosh OS X Beachballs!
Macintosh Slowdown Solutions
Macintosh OS X Slowdown Solutions
You can expect your Mac to be slow normally for a few days after upgrading to any major new version of the Mac OS. It is re-indexing your hard drive, re-forming caches, etc.
It will also be noticeably slower if you've moved from a pre-Mojave OS to Catalina, if you have an internal rotating disk hard drive (RDHD). Mojave and Catalina automatically reformat your internal hard drive as APFS, which is optimized for SSD's, and really not optimized for RDHD's.
You many also have stay-resident software installed that is now outdated. Look in System Preferences --> Users & Groups --> Login Items
and see what's there. You may want to uninstall all of it.
If you have any software that runs at a low-level, like anti-virus software, or disk utility software, uninstall it using the developer's uninstaller.
If worse comes to worse, you can use Recovery to fall back to the OS that your Mac came with:
About macOS Recovery - Apple Support