First off,
Yes, yes, yes, absolutely use 5W-20. It is NOT too thin...ignore the people who are scaring you with that argument. They do not know what they're talking about. It has given excellent performance, longevity, and UOA (used oil analysis) reports, plus better fuel economy. There are many examples, but one in particular was a policeman who used nothing but Motorcraft 5W-20 on his patrol car (lots of hard use, idling, high speeds, etc.), had over 200K and it was still going strong.
If you want to switch to synthetic, now is a fine time and Pennzoil Platinum is a great oil that can be had for a great price on specials (like now at Advance Auto it's BOGO - buy one get one free). But depending how you plan to drive your car and how long you want to keep it, any good brand name dino oil or blend (like Motorcraft is excellent, but so is Pennzoil, Havoline, TropArtic, Quaker State, Exxon Superflo, Formula Shell, etc.) will serve you just fine.
IMHO, synthetic is only "necessary" for severe service, like high-revving, racing, towing, turbo, lots of stop and go, short trips, etc. or longer drain intervals. Or if you're like me and you just want to be anal and use what you think to the be the very "best" to squeak out as much as is humanly possible out of your engine. For the average driver who may keep his car 100K to 150K and has normal driving conditions, synthetic may be a waste (unless you want extended drain intervals).