Firstly, you can play game online - nothing will happen.
Some games (original discs) may ask you to update your system menu. Don't do this and you will be fine.
Those games require system updates to play, but you actually don't have to update your system! A handy thing called a cIOS is all you need to play the game - you install it and your game will work.
You should post in the "introduce yourself" section as you will get plenty of info and links to guides.