Except Megamek does not print the rules. You can figure it out what is going on, but it might be confusing.
Or, if you're like me and just enjoy playing with physical minis and real dice with real paper and pencils....
Best way to start is the "Battletech introductory boxed set" (Google it). This has the minis, maps, and basic rules. Everything you need for a game.
The next step to get deeper into the game is the core rulebooks. Starting with "Total Warfare". This include the rules for things like battle armor, tanks, and aerospace.