Time Machine is stupidly easy to use. It is my main back up method, after years of using third party apps like Super Duper and Carbon Copy Cloner that took a bit of management. TM has saved my ass a number of times.
Yes in TM options/prefs you can select which folders to ignore. I ignore system files and folders and leave space for work files. I work in video so I have some massive project folders. I have clean functional clones of freshly installed OS drives I can restore if necessary and then pull all my working files from TM backups.
And yes, any HD that is mounted and recognized on your desktop can be used as TM drive. Also there are NAS options that work with TM too. I have a 4TB Seagate Central that my wife and son can both connect to that automatically works as a TM volume over the network. It’s a bit slow as it’s over wifi but they wouldn’t back up otherwise, so I set it up for them and they can forget about it.