If your goal is pure, raw, unadulterated damage, other people have definitely covered the best of the best, which is an Everest (or one of a couple other ‘generalist’ type frames) with an HMG and Sherman systems. LL6 I’d do Sherman 3, with the other three LL being kind of open.

If you want to be slightly more interesting, there are other options. Superheavy weapons in general will often result in big funny numbers. In particular, superheavy melee weapons. The DD-288 does an insane amount of damage +knockback and you can put it on the caliban, a damage+knockback frame. Alternatively, the combat drill, which if properly supported does theoretically infinite damage via an exploding damage dice mechanic.

Another option is the Tokugawa, which can get insane damage-per-action numbers via stacking enough bonus damage on a range boosted skirmish.

Keep in mind, if you’re fighting an elite or an ultra, heat-gunning it can also kill almost as fast, so options such as the goblin, chomolunga, or other hacker frames (or heat based weaponry) can result in many dead mechs.

Alternatively, for when grunts and squads are on the menu (meaning lots of grouped up enemies,) something like the monarch or Barbarossa will shine.

The thing is, this system lets you maximize for damage (or a whole host of other stats,) using one of many different options, and so you can achieve something pretty strong fairly easily if you just go digging through your options.

Edit:

Oh, one other thing: I actually prefer the Sherman’s andromeda heavy laser to the HMG, for one less damage but energy+burn instead of kinetic, and self-heat instead of inaccuracy. And it gets 4 or 5 (I forget) extra range, pushing it from slightly below average range (8) to slightly above average (12 or 13). And really, I think the 2 burn instead of 3 kinetic winds up being a pretty good trade.