It's easier than you think.
For starters, just about any loco from any manufacturer will run in Conventional Mode. (This is a fancy way of saying "will run with just a regular transformer".)
Lionel and MTH have competing/rival command control systems that GENERALLY are not compatible with each other IN COMMAND MODE as the locos come from the factory.....BUT can be made somewhat compatible with each other in a limited way if you utilize certain ADDITIONAL electronics. (Again, you can always run competing/different locos from any company in Conventional Mode.)
Odyssey is basically electronic cruise control for Lionel (TMCC and Legacy) locos and those from other companies who license TMCC from Lionel. Odyssey II is basically a refined/improved version of Odyssey. With either, the loco will not change speed regardless of changes in track voltage. (This is in contrast to trains running faster or slower as your track voltage fluctuates.) They will also run at surprisingly slow speeds, especially with Odyssey II.
TMCC is Lionel's original command control system. Legacy is a newer, more feature packed and more complicted command control system.
Legacy is designed to run any TMCC equipped loco with almost all of it's original features. Also, any Legacy loco can run in TMCC but not all of its features will work. The are not mutually exclusive. Quite the opposite, actually. By design. Just think of it this way: They are compatible with each other. Legacy locos have more features but when run in TMCC, not all are available to you.
Dizzy yet?
Here's the easy part: Hooking up TMCC is simple. You'll need a transformer, a remote, and a base.
You simply hook up a wire from the base to the negative wire/lead that runs from the transformer to your track. The negative wire/lead needs to be connected to one of your outside track rails. You will want the center rail to be positive. All of the TMCC signals are generated through your negative wire/lead on the outside rail. (Be sure to also actually plug both in!)
There is a great book on the matter by Neil Beseiloff (sp?) that is a terrific resource/starting point. It details how TMCC and DCS (MTH) operate....but it was written before Legacy came out.
If your new to this, I would simply start with TMCC. It's WAY simpler.