My first oil change was Valvoline Synpower 10w-30 (synthetic) and a Wix filter.
My next will be Mobil 1 10w-30 and either a Wix or Purolator.
I prefer synthetic because I drive what's called extreme driving conditions. Winter cold start ups and short trips(lots of condensation in the engine in the winter). And it was on sale at the time and I started looking into it and eventually got myself into buying synthetic. Synthetic oil IS a better oil, period. It's like dex III and VI. (Knowing that, I still use III for certain reasons, just as some engines should seriously stick to conventional) It's better in more-so extreme conditions, many will not see these conditions so it may not do a whole lot for them(for the extra money they pay) besides extending the change interval. Plus there are more detergents and bla bla bla. I pay $24.97 for 5 quarts of full synthetic Valvoline/Mobil 1, so I can't complain about prices being too high.
If I paid for the cheapest conventional($13.97 for Mobil super) and went 3k; and the cheapest synthetic($20.97 for Quaker State) and went 5k, there's not much more money spent for oil that is a little better(for my engine, not all engines though)
Definitely don't use synthetic oil in worn engines because it's properties are a little different (Just like why I don't want Dex 6 in my 110k mile 02 trans) It can cause the engine to make more valve noise from a faster flowing oil, and cause seals to seep more. When I first got my car, as far as I knew, conventional was the only oil ever used in it. When I switched to synthetic, my valve cover gaskets began to seep more than twice as bad. It went from occasionally smelling it, to actually seeing smoke. Point being, there are certain places synthetic will be an improvement over conventional, and some places it will be worse. Choose carefully lol, but you can always switch back.