This is how I deal with experience in my solo campaigns that I've played, typically playing against myself using megamek.
Take my formation of warriors (more often than not they're mercs). Use whatever rules I want to use to determine piloting and gunnery during the units formation. Once it comes time for choosing a contract (an one is selected) each member of the unit gets one experience point. Call it a participation point in case their lance jus doesn't get used during the run of the contract. Then each person who survives a "drop" or a match/battle or whatever else you wanna call it, they get another point. Add one more point for each kill they achieve during that match.
After each contract those that have enough points can turn them in for improvement to piloting and/or gunnery skills - piloting costs four points, while gunnery costs eight. Further, the two skill points must be "adjacent" to each other; I.e. 3/4 or 4/5 etc is ok, but 4/6 or 1/4 is not. So basically every 12 points earned increases a pilots skill level.
New joining member start at either green or regular (at extra purchasing cost based on the rules in play that determine gaining new members).
Over the course of time your units overall experience level will maybe fluctuate wildly but those that have been around for a while are likely to better at their job than the new boot.
Just my "house rule" and one that is fairly easy to run with, IMHO.
