You can't outmaneuver yourself is actually a good starting point. That's why you have initiative. Trying to beat yourself is one of the ways of figuring out how to min-max moves on each side. And, you shouldn't be ashamed of it.
'If I move here, then that side is almost certainly to have x Mech move behind me. Start with that! This will be the time you will figure out which Mechs are best used early in a turn, and which you want to save for as late as possible.
If you really are interested in story-driven engagements, then, yes, you need to chose a 'hero' side. Give the hero a few things, such as an 'Edge' pool, mostly to keep that hero alive, more than anything. See where it goes, and then derive consequences from losing or winning the match.
If you have a brainstorm moment in the middle of a turn where you realize you could have moved better, don't be afraid to walk the turn back to that moment and make it happen. It's effectively a casual game, so you shouldn't be worried about running it tournament-tight.
Once you start the story going, it's your world, you can do what you want with it. This would be your moment to have fun with coming up with a narrative.
I had to learn BattleTech from solo play. I first started by playing each side to the fullest, because the outcome didn't exactly matter to me. I wanted to see how it would play out, the dice being the random factor. Eventually, though, the idea of pilot improvement over a series of games made me want to come up with a pilot to nurture and grow in combat, and it kept me coming back, first to my solo games. Eventually, I found friends to play with, and not only were they enamored with the character I came up with, and the ride I wanted him in, but they wanted to do the same.
Eventually, balanced games went to the wayside, story-campaigns with our custom characters being the big focus. Now, I've been using the Low-Altitude map concept in Aero to set-up larger engagements with Battalions to a side maneuvering into battle range, allowing for potentially uneven battles turning into grinders while other forces flank to reach key objectives which will change the nature of the larger battle.