You're better off getting Taiyo Yudens, Sonys, Verbatims, Maxells or Ritek. Check here for media IDs and make sure you buy it from a good reputable site like rima, supermediastore or new-egg. The link I sent you I believe also has sites listed and suggestions on where you could go to buy your media brands. As for really cheap brands yet they work decently, you could try to get some TDKs or Memorex and hope they code out as RICOHJPNs and not CMC MAGs, but I suggest you to just stick with the top-tier brands for better quality burns and such. TDKs and Memorex aren't so bad, but they can't compare to the 1st-class DVD brands you can buy for a bit more.
The software is practically free. Just google it or something. As for where to find information on the software aspect of backing up games, look around the many stickies listed under the PS2 - DVD Backup Discussion section here in the afterdawn forums. You'll see them in the first page when you click on it and enter. Good luck with it.
As for software, you can use like DVD Decryptor, IMGBurn or Nero. PS2 CD games or PSX games with Alcohol 120% I think although I'm not too certain either.
