From the drive train, Chain/Cluster/Chain ring(s) would normally be enough and should be done together, or the old components would wear out the new one quickly. Although you can get by not changing the chain ring if you replace the chain often, if the chain is badly worn, a new chain ring is strongly recommended.
Check the pulleys on the derailleur for wear, and replace if needed. The derailleur itself may or may not be worn out - Unless obviously sloppy, I would leave buying a new one till the new drive train was in place, I had replaced the cable and checked hanger alignment and still could not get it to shift well.
Based on the wear on the drive train, I would presume the bike has been somewhat neglected. Check the BB and pedals while the chain is off. Check the headset and wheel bearings, ideally clean and repack.
Unless in obviously new condition, I would replace shifter and brake cables as they are cheap, although if you don't have cable cutters and they are working well its possibly more effort than it worth.