Where did you hear going back and forth will gum up your engine? Synthetic oil is designed to work with conventional oil. Mix them, match them, run whatever you want, however you want. Just do it.
5w30 is on the cap, and in the manual. If we're talking brands, I like mobil 1 full synthetic. Just know that if your car has a leak somewhere, then synthetic oil will drip through the leak faster, and make it appear worse. That's what happened to me, and it showed me that I had a valve cover leak.
Source:
Eric the Car Guy Conventional vs Synthetic