Seven and eight speed drivetrains use the same chain, completely interchangeable. Chains for derailleur-equipped drivetrains are usually labeled as eight speed, nine speed, and ten speed these days, with nine speed chains being narrower than eight speed, and ten speed chains being narrower than nine speed. As for 5, 6, 7, and 8 speed drivetrains, they can all use "eight speed" chains.
In regard to chain length, here's a link to Sheldon's site explaining the process for sizing a chain.
http://sheldonbrown.com/derailer-adjustment.html#chain