MacOS – iMessages app is missing after update of OSX to Mountain Lion

The Time Machine backup should do a pretty good job keeping all of your documents and most of your settings and should be backwards-compatible*, but I recommend making a complete, bootable backup of your previous system so that you're guaranteed to be able to restore your machine to exactly as it was before updating.

I'm a fan of Carbon Copy Cloner (free trial) for making the backup. Back up to a clean disk or partition using CCC and tell it to copy everything. It will also help you clone your Lion Recovery HD onto the backup disk.

Once the backup is done be sure to try booting from it to make sure everything worked.

*Should be, but I haven't personally tested.

Try logging into the machine with your display hooked up with HDMI (just so you can login), then switch over to VGA. Then try CMD + F2 (brightness up) to force detect displays and see if it switches over.