[LS short box]

As for what to do here's my .02.
Replace the oil pump.
Judgement call on replacing the timing chain. They are pretty cheap.
Pull the other head and check all the lifters. Pull the cam and check for wear. Maybe replace the lifter trays since they are cheap.
If you have a machine shop near by have them mic the cylinders to determine wear. May have been bored since you can still see the cross hatching.
Depending on your budget maybe a small cam? Means new better push rods and springs.
Good luck with your project.
Maybe pull a few rod caps to check bearings for wear. Doesn't cost anything.
Pull main caps and check for wear? Only cost is new crank bolts.