You can simply buy a games script with lots of flash games and host them anywhere. You can go to flashgamescript.com or search for game scripts in google.
If you need some games to get you started - I have around a GB of .swf files free for download on www.torex.org - just click on the "free downloads" section
There are tonnes of game scripts available out there with thousands of games around $20-$50 range. gamescript and phparcade are two solid scripts where you can get started.
Buy a gamescript, a games database, hire a designer for a nice layout, buy some hosting and your done.
Thank you for the tips! 1. Do the games online take a lot of bandwidth? 2. Do they take a lot of Server Resources? I have a web hosting company already with 2,000 G bandwidth.