I fight incompetently, so far as I can tell.
Other than that, I end up gravitating toward brute force like Ogre describes; you know how it is with plans and contact with the enemy. When I try to achieve flexibility by teaming complementary 'mechs with each other, like Griffins and Wolverines, I get one focus-killed first and then the other hard-countered, so instead I'm most comfortable using a homogenous force of JOATs and simply trying to focus on whatever seems like the most [powerful * exposed / durable] target, because anything fancier than that is too much for a fleshy-headed mutant like myself to keep from flying apart. Similarly, I'll split my force into two or three groups to attempt a half-assed suggestion of a pincer movement if the target's slow or to cover each other's backsides if the target's fast, but I'm sheepish about letting anything get more than a turn away from help from every one else, rotating 'mechs as they get worn on unevenly.
Toys-wise...
[...] stubbornly one-dimensional. He focuses only on heavy heavies, well heat balanced, and with strict range bracketing. [...]
That sounds a lot like me, except that I prefer my heavies in wrong weight classes, and I also like them crude killamajigs: for canon 'mech examples, overgrown "heavies" like the Beemer and Thug are especially forgiving of my more-than-occasional mistakes, while OTOH "real" assault 'mechs like the Awesome can just slug it out pretty well with anything.
Right now, I most enjoy an "underweight heavy" kinda like the Centurion: cheaper than "real" bruisers like the Orion, which means I can have more of them. It's a bit less tanky and more blasty than I'm naturally inclined toward, but combines most of the capability and user-friendliness of heavy troopers with most of the sheer bang-for-buck of ass-plodders, and I consider a demi-company of spunky mediumweights an upgrade over a lance of heavyweights. (figuring roughly 4 Megabucks or 1.2 kiloBV per 'mech vs. 6M CB or 1.8k BV) Most importantly, it makes gameplay feel more decisively violent instead of taking forever, so I'm actually likely to play a bit of Battletech occasionally.
My ideal "Goldilocks" battlemech is optimised to be the perfect balance between glassy-blasty brutality and wishy-washy indecisiveness: a mediumweight with modest 4-6-4 mobility so it has lots of armor and heat sinks for its cost, built around the classic PPC + ML combo so it rarely needs to control engagement range.
I especially like when fast light brawlers so cleverly stay outside the lasers' short range, so that the PPC are effectively upgraded LPL. Being at the top of the AMM:TMM breakeven brackets for walking and running means it fights with equal aplomb either running and gunning or shooting and scooting, while an indecisive blend of reachy peeper and powerful laserball lets it work equally well as a fire 'mech or a scrapper- not terribly well in either role, but every one can contribute to whichever role is more needed, or the most worn 'mechs can rotate from the front to the back and/or switch up to higher movement modes. Small size for this motive profile lets me get the most out of the per-'mech overheat capacity and 10 "free" heat sinks, while the bracket setup gives it a zombie-like systems redundancy, if only at middle ranges, that's much-needed for such an obnoxious 'mech.