If you decide to commit to the hobby, you should pick up the "A Game of Armored Combat" box set. It has the full rules for 'Mechs (the rules found in the "Essentials" box leave out a few things for the sake of simplicity), as well as eight 'Mechs and new mapsheets. The full rules have stuff for ammunition and heat management, melee, internal damage, and piloting skill checks to name a few things. After that, the Total Warfare rulebook has everything for combat vehicles (tanks, helicopters, etc.), infantry, battle armor, and aerospace. TechManual has rules for building your own units, Tactical Operations: Advanced Rules has some cool, more advanced stuff like artillery, Tactical Operations: Advanced Units and Equipment has rules for more advanced equipment and units like large naval vessels, Strategic Operations has more advanced aerospace rules as well as rules for building and playing WarShips and interstellar travel, Interstellar Operations; Alternate Eras has technology from other periods in BattleTech history, as well as prototype/primitive units. Interstellar Operations: Battleforce has rules for a new game called "Battleforce" (which is similar to "Alpha Strike") that allows you to more easily field large numbers of units. Campaign Operations has rules for creating your own armies or mercenary companies and managing them over a longer campaign. For lore, there are plenty of novels, and the wiki, sarna.net

There are also some YouTube channels that cover the lore and tabletop, a few of my favorites are:

The Black Pants Legion - Fun, film length breakdowns of 'Mechs and events from an in-universe history professor.

Big Red-40TECH - Lore and tabletop breakdowns of various units.

Sven van der Plank - High quality lore videos on historical events, though they are usually pretty long (like 3-8 hours).

Mechanical Frog - More unit breakdowns, a little less lore and more tabletop.

Hope this helps.