I have a MacBook Pro that is just being ridiculous, so I'm planning on erasing the hard drive and restoring from a Time Machine backup. I hear that Time Machine will only restore from backups that have been made from the computer.

If I erase the hard drive in Disk Utilities will it think the Time Machine back up is a different computer?

Is it possible to perform a clean install and retrieve all my personal files back from the Time Machine? Rather than just reinstall around my personal files?

Or even better is it possible to do a clean install and then pull files manually from the Time Machine backup as and when I need them?