Welcome to the forum!
Basically, the best way to boot a backup is a modchip - as you just put in your disc and play ala. normal PS2. With the no modchip techniques, you have to swap discs, install silly flip lids and mess about - and even then it's not going to work with every game...
Modchips these days also offer WAY more features than just playing backups... with the best chips, you can launch homebrew from HDD, Memory Cards etc, interface with Xbox-style dashboards etc (and as you're going to have to void your warrenty anyway...) you may as well install a proper modchip. The best at the moment are the Matrix Infinity and the Crystal v2.0.
To copy PS2 DVD's, the best solution is DVD Decrypter as it's free. However, pretty much any standard copier (such as Nero, RecordNow, and the latest CloneCD) will all do a fantastic job!
* and yes, you're right - maybe we should update the sticky's a little
*