Monterey freezes after I choose where to install the OS.

Try the following:

#1 - boot into Safe Mode according to Start up your Mac in safe mode - Apple Support.

NOTE: Safe Mode boot can take up to 3-5 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

#2 - go to the System/Software Update preference pane and begin the download.

#3 - run the installer from the Safe Mode.

I've had better luck from the Safe Mode because I evidently have some 3rd party software that interferes with the installation.