Here's what you need;

1-2 PlayStation 2 controllers (depends wether or not will you game by yourself or with friends/siblings)
1-2 Memory Cards (8 MB is a standard one, but there are also bigger ones like 16 and 32 MB. I'd stick to the original 8 MB just in case ^^)
Cable from PS2 to TV (even if you have an LCD TV, make sure that it has a SCART or RCA port!
Examples; https://images-na.ssl-images-amazon.....1Bafxx80aL.jpg
http://image.dhgate.com/upload/2010.....1063767743.jpg )
1 Power cable that connects the PS2 to your power socket

And last but not least; videogames! :3

I was thinking a little bigger. I was gonna go for a light gun too in case I come across Time Crisis 2

Ahh, I see :3

If you're gonna go that big, here's what else you can get;

EyeToy - a PS2 camera that follows your movements (https://upload.wikimedia.org/wikipe.....PS2-Eyetoy.jpg )
Guitar Hero Controller - for all those wonderful Guitar Hero games, wireless or not! <3 ( http://i1009.photobucket.com/albums.....lection031.jpg )
Buzz! Controller - it's a those quiz show games if you like them (http://images.bidorbuy.co.za/user_i.....151510_430.jpg)
DJ Hero Controller - wanna know how it feels to be a DJ? Check this out too! (http://gamerinvestments.com/video-g.....troller__3.jpg )

*gasp* I LOVE EYETOY!!! The rest is just shit tho XD

And what games are absolutely necessary for a PS2?

Here are some of my faves;

God of War 1 and 2
Silent Hill 2, 3, 4
Shadow of the Colossus
Metal Gear Solid 3
Persona 3 and 4
Final Fantasy X
Tekken 5
Bloody Roar 3 and 4
Kingdom Hearts 1 and 2
Sly Cooper 1,2,3
Resident Evil 4
Destroy All Humans!
Cold Fear
Ratchet and Clank 1,2,3,4
Flatout 2
Gran Turismo 4
Tourist Trophy
Obscure 1 and 2
Devil May Cry 1 and 3 (2 is a bad one ;w;)
Black

Question tho; are you gonna buy originals or download them yourself?

This is a pretty good list, if I do say so myself.

And to add to what Mintlovepaw is saying, you can also play PS1 games on the PS2 :D But they need the PS1 memory card for that (they're super cheap online)

I love the PS2 so much ; ;

Really!? Oh heck, I'm gonna play the heck outta that system then! They had a whole crate full of PS1 games~

I'm sure most (if not all) are playable on the PS2, I still play mine on it! Soul Reaver, Abe's Oddysee/Exoddus and ofc the orignal Resident Evils are all must haves!! Enjoy!! :D

Will do hon

Dang buddy. Hit me right in my heart with this one. I loved my PS2 and Time Crisis 2&3 were my jams. Loved playing the complete story of Time Crisis 3. Bloody Roar and Tekken were also among my big time faves.
One thing that I don't think was mentioned though is if you want to play online, there's a separate Internet thing that you'd need to get.