Battletech overview & what I think you should get!

About BattleTech: A Game of Armored Combat, from BoardGameGeek:

In this introduction to the BattleTech game and universe, players each take control of one or more giant walking war machines (BattleMechs, aka 'Mechs) and battle until their opponent is destroyed or until the scenario objectives being played are completed. In 2019 the old BattleTech Introductory Box Set was replaced by two all-new box sets. The second of these (after the Beginner Box) is A Game of Armored Combat. AGoAC comes with eight 'Mech miniatures (made to a higher quality level than the previous generation of box set miniatures). The AGoAC rules cover introductory weapons and construction technology, and the standard BattleTech ruleset for 'Mechs. An expansion for this set, the BattleTech: Clan Invasion box set, adds more advanced technologies and introduces the Clan factions. In terms of rulebooks, the intended follow-on from this box is either the BattleMech Manual (for more advanced but still 'Mech-only play) or Total Warfare (for combined arms play featuring 'Mechs, combat vehicles, infantry, air support, etc).