You can update either through the PC Suite, or you can take the phone to an LG service center or you can flash a ROM which has the android version you want.

I never got the PC Suite to work, so I had to go to the LG service center to update from 2.2.1 (my phone was already 2.2.1 when I bought it) to 2.2.2. The guys at the service center said I'll loose all my contacts, apps, data, etc etc after the update. The same happens when you flash a custom ROM.

Anyway, since you're rooted, you can backup your apps, contacts, app data, and 99% of your settings.

And are you sure that your Optimus One came with only 2.1? I was pretty sure it had 2.2 from when it was released. Its kind of odd that your 1 month old O1 has 2.1 when my 2 month old O1 had 2.2 from the start

 

If you dont mind loosing the app data, then you dont have to use titanium backup. Then you dont have to root and LG will update for you with no problem at all.

Even if you root, you can still get the official update if you use LG PC Suite. If it cant find your phone, and you rooted, then you can always undo the root and take it to the service center. Just be sure you wont leave any hints that you rooted. Usually they wont even check if its rooted.

You can jump straight to 2.3. You dont need a giude if you're planning to update to a stock ROM. But if you're planning on flashing a custom ROM, just google and you'll find lots of tutorials. The process has been explained in simple terms and quite briefly here.