Synthetic oil will not stop a dry lifter tap. If its a dry lifter noise run some goop in the engine, stp,whynns friction proofing,the extra cost of synthetic oil will not do anything the Pennsylvania grade oil will do. Its a ten year old throw away car at this point with high miles just run it. Keep the level where it should be and keep the oil clean. Save your money for a new motor don't waste it on synthetic oil.
If you want a better grade of oil change over to a 15/40 like shell rotella -T its a diesel oil with additives. It will be a bit heavier but will quiet the noise and keep the thing clean. Most guys I know and even the cops run 15/40 in the fleet cars, they are run hard and never have a problem because of it. :howdy