Well, better late than never, i suppose! Congratz for getting the former most popular game console within the world of video games. ;)

As for the games... Definately God of War!! If you are even in the slightest into the Action & Adventure genre, you have to play both of Kratos legendary adventures! But im gonna warn you for god of war's sake... If you cant stand epicness like superb setpieces, an amazing sense of scale, brilliant boss battles, fantastic soundtrack, intense combat system, good gore and much more, this isnt for you! :P

Other than that: Ratchet & Clank is a great choice. But i recommend to get and play the very first before anything else in the series. Its important to experience the very beginning of the intergalactic duo by witnessing their first met. This way you'll have a better understanding of the story and enjoy the sequels even more. The latter because Going Commando as well as Up Your Arsenal adding several improvements to the gameplay, overall increasing in quality. =)

Ratchet & Clank is a good start! Next games should be Metal Gear Solid and God of War.

Good stuff! Dark Alliance is not easy to come by these days, I've sunk a stupid number of hours into it. I still hear the stupid rambling dwarf merchant to this day just thinking about it. "Swords, axes, bows...we have everything you need right here." I was pissed when playing Diablo 3 couch co-op and realizing that only one person could shop at a time, whereas DA let two players shop simultaneously like a decade earlier.

I'd start by enjoying the the PS1 library before moving to the PS2 games because the PS1 had so much to offer! (especially if your a Jrpg fan!) It would be a shame to skip it!

Congratulations

Congrats :) PS2 was a great system back in the day, my only fear is that you may be put off of the Playstation brand if you play some of the older exclusives with the expectation that they would be great by today's standards. Despite what people say, a nostalgic memory is often different to reality and game quality has in many cases improved!

You should really get Silent Hill 2. It's one of the best, if not the best survival horror ever made, with a complex story, amazing characters, a fascinating lore and an ambiance like you've never experienced. Also, amazing OST.

Apart from that, damn. Looks like you'll have a busy summer. Great choices though, and have fun !