I got my fist PS2 last week (never had a PS1 either and only save my games on the hard drive in my Xbox, so I'm new to this memory card thing). I bought one of those yello Nyko PS2 memory cards for it ...
PS2 games require a PS2 multitap, but can often (but not always) use PSX Dual Shock controllers, however there won't be any analog support for the buttons (the analog sticks should work just ...