The first novel published was The Sword and the Dagger (Armin Shimerman, 1987). It is out of print, poorly written, and its events are largely retconned. The second was Decision at Thunder Rift (William H. Keith, 1988) – which is excellent, but it is a prequel about a tiny mercenary unit (the Gray Death Legion) that has almost no bearing on the galactic civil war.
This is an excellent question, as BattleTech is one of the most sprawling and complex fictional universes ever created. Unlike a single linear series like Harry Potter or The Expanse , the BattleTech novel line is best understood as a historical chronicle of the 31st and 32nd centuries, told through interlocking miniseries, standalone novels, and multi-author anthologies.
To simply provide a list is insufficient. One must first understand the of publishing, as the "order" changes drastically depending on your goal (publication date vs. internal chronology).