You're talking about two different ways of interacting with a Time Machine backup: restoring and migration.
Restoring from a Time Machine backup essentially makes your computer identical to the state of that backup, with some caveats. Performing a restore from a restoration partition or from a disk will not give you a clean system. You will have all of the same problems that you had when you last backed up.
Migrating from a Time Machine backup will take certain parts of that backup and move them to a freshly installed system. Migrating will let you retain a clean install, but there is always the chance that what you migrate over was the problem in the first place. No matter what you choose, there can always be problems. From my personal experience, however, I can say that the things that are both least essential and have the most potential to cause problems are "Settings" and "Other Files and Folders".
To answer your specific questions regarding graphics hanging and performance, the best option you have is to migrate your user folder, see if the problems persist, and then migrate your applications. You won't be able to create a user and then migrate to that user later - the migration will just create a new user when you try to migrate. The "Settings" are actually just system settings, network settings/profiles, and printers - in other words, nothing that has anything to do with your user account.
Sorry if that answer was a bit rambly. ;)