Important note for BattleTech:
BattleTech is a tactical wargame. Primarily built for 1v1 scenarios where you each control a handful of mechs. Very little RP built into the system.
What you'd be looking for is the MechWarrior TTRPGs which are set in the same universe. Either "A Time of War" or "Destiny."
Destiny is gonna be a very narrative, rules light system. Much more focused on telling a story. Quick and easy, and very collaborative. That's gonna feel different for the players and GM if you're mostly familiar with DnD.
A Time of War is gonna be more crunchy tactical wargaming. Lots of dice. Like DnD it's mostly built around combat, but it's gonna be more in-depth, closer to the DnD 3.5 levels of crunch.
Lander FWIW is very fun and pretty easy to get into. There are some good prewritten adventures that do a good job to introduce both players and the GM to the system.