WHDLoad will be your best friend. It'll allow you to run loads of old games on more recent hardware with great ease. That way you don't need to fiddle with degraders, and rebooting, and disk swapping whenever you want to play something. Just make sure you've got enough Fast RAM - 4MB is usually enough.
As for systems... cheapest and easiest to find will probably be an A2000 or an A1200, but the A2000 will need significant upgrading (and cash) to be usable as an internet machine. An A1200 with a 68030 accelerator should suffice for what you're planning to do. Adding a CD drive to a standard A1200 can be a bit challenging, though.
Welcome, and enjoy your stay. Don't hesitate to ask for help!
