Here's my take on it: it's very straightforward, so you won't see anything special here. Just a straight combat character, who should still be theoretically capable of beating the game playing solo, while taking advantage of those high stats.
The first 6 skills:
*Dodge
*Small Arms
*Mecha Piloting
*Mecha Gunnery
(i.e., taking both mecha and personal combat, but going for the absolute minimum skill investments in both. Finding a Laser Rifle or other such personal weapon early in the game is left as an exercise to the reader. Optionally replace Small Arms with Heavy Weapons, and Mecha Gunnery with Mecha Artillery, if you'd like to take advantage of your non-horrific Pe, but making Mecha Artillery work in the early game is tricky.)
*Conversation
*an XP-generating skill. Code breaking, Mecha Repair, what have you. Medicine, Mysticism, Performance, or Investigation if you'd like to tailor yourself towards a skill-related mission.
It should be reasonably doable to simply play a straight combat character, starting with the arena and moving onward. I normally start a game with my combat skills around +2 or +3 and my relevant combat stats around 15-ish, but it should be possible to start with combat skills at +5, and stats at 1, and simply raising your skills ASAP. You'll have to go for a career as a Lawyer, simply because most careers which include combat skills include too MANY of them for this minimal build.
Of course, you'll probably have to fall back on personal combat and sewer-diving as your mecha is destroyed, but once you've saved up for GARU serum (relatively easy with a Lawyer!), you'll be a combat monster and can play a straight violent game with a bare minimum of non-violence-related missions.
The lack of speed, and lack of Initiative, will make you horribly slow in the early game, but you can overcome this simply by charging at full speed across the battlefield, all the time. Of course, if you don't like taking advantage of game quirks, then you should replace your XP-generating skill with Initiative, simply to have a decent chance to survive.