My opinion (and it's strictly opinion
) Keep using the zinc additive and run full synthetic if you can afford it. You don't need to change the oil every 3000 miles like the old days either. I went with 5000 miles between changes on a turbo engine that wasn't treated kindly. My Volvo's ran 7500 miles between changes on turbo engines. They were treated a little nicer though.
If you want to run the cheapest Walmart oil then just change it more frequently but still use the zinc additive. It helps to protect your cam lobes.