They are TMCC & Legacy by Lionel for their modern S Engines equipped with them, DCC for some locomotives equipped for it. DCS by MTH that will run Lionel TMCC engines and the F3, which is their only engine so far in S. FlyerChief, the new Lionel system, operates both on AC and DC.
Gilbert, most older Flyionel products use AC with transformers. American Models run on AC and DC if equipped, but no operating system.
The big question is are you going to be HiRail or Scale? This makes a huge difference in what you will buy and operate.