Which Rods and pistons for a 360?

Forged are better. No question. Hyper's will certainly work for what you describe , and I know they say they will take a small shot of juice. I think you will want the tune up to be correct if you go that way.
Stock rods with good bolts will take all you describe.
If the piston weights are significantly different...............hell , even if they aren't , I'd have it balanced by a quality shop.
As far as being worth it to bore , it really depends on the shape of the bores. If they will clean up with a light hone and you can still get inside recommended piston to wall , you are golden. If it is an old and / or tired motor , you probably want to go over size.