Need help picking the right rear derailleur and chain for Giant Escape 2
All 8- and 9-speed Shimano mountain derailleurs are compatible. Just pick one that you like. The one thing to worry is long cage versus extra long cage, and unless you know you have an extra wide range of gears, long cage is fine.

The chain is also fine. If you are changing the chain because is worn out or "stretched", you should probably replace the rear cogs too.