A good way to save money on online games would be to go to a rental store (blockbuster, Hollywood video, etc.) and rent the game before you buy it to see if you like it.
Another way to save money is to buy the game for the PC.. xbox live charges people to play online. Games that are available for both xbox and PC (call of duty, halo 2, etc) will allow you to play online for free as long as you have a windows live ID (free)
PC games on the other hand (world of warcraft, etc.) will often offer you a 14 day free trail to test the game out and see if you like it before you spend so much a month to play it.
The Playstation3 comes wireless ready, and allows you to surf the web and play online compatible games for free. hope this advice helps!