Remove the hard drive from the dead iMac and place it in an external carrier or use a universal adapter to attach it to your new machine. Once you do that you can transfer data from the old drive to your new one.
External carriers and adapters are sold at many places. On line - NewEgg, Amazon, etc. Locally you can find them at stores like Fry's, Best Buy, and so on.
As for a backup strategy, use the free Time Machine which comes with Leopard and Snow Leopard. It's an excellent way to back up. You will of course need an external hard drive in order to use Time Machine. You can always use your old hard drive and the carrier it's in after removing what data you need from it.
Regards.