Ok here's how you maintain that thing.
-Never turn the system off by hitting the main switch on the back while playing a game
-Make sure your disks have no dust, fingerprints and any of the sort on it.
-Place the PS2 in a well ventilated area. This thing is dust magnet and dust is the leading cause of the famous "Disk read error". Use canned air and/or vaccum the vents around it to keep dust from quickly building up in your machine. (No matter how hard you try, dust will always get in it, this just keeps it from building quickly.)
-Never use non-sony licensed products or mod your PS2. Sony are such nice guys that if you take care of you machine, they can repair your system for free even after the warranty is expired should anything happen to it.
-Register your PS2 and network adapter with sony by using the network adapter utiltiy disk, calling sony or logging on to their website at playstation.com. You'll get cool stuff from them like newsletters, demos and the sort.
-Last is basically don't do anything stupid like putting stuff on top of it, drop it, shake it, stuff like that.
You basically have all you need for a PS2. Get another controller if only have 1 and get more games. You can't go wrong with the greatest hits titles. (The games with the red tags on it)