I just posted about a campaign I ran in the early 2000's, so I feel I may have something to contribute here. Please feel free to ignore some or all as you like!
Battletech is the GURPS of wargaming. Simple game rules/mechanics, and the ability to layer on just about anything you need for rules for specific situations. If you are looking for something light, you can make it light. If you want something heavy, it can do that too. But I think the most important thing for this or any ruleset is to stop, take a step back, and ask yourself what it is you are looking for out of the game.
Are you trying to tell a story about how a world is in rebellion? How players are coming of age in a civil war? How supply officers became the most important part of any military from WWI and beyond by tracking every round of ammunition spent in a battle? What are you trying for out of the game? Once you have answered that, you can figure out what points to highlight in your game, and the rules can be tweaked to resolve each part of the story.
For example, in a Battletech campaign I ran over about six months, the story was about a band of Mercenaries going to a backwater world to cause just enough havok to draw off troops from another world that was the actual target. So they had to do damage, but not so much that the world would be written off. So I came up with a dozen 'targets of interest' and gave each one a military value, a morale value, and a resource value. Then I made a pyramid of totals, and made the spaceport, the capital city, and the main military base the highest values and went from there. I put them all on a map, gave it to the players, and let them decide where they wanted to land and start their campaign from. Secretly, it was all very arbitrary because we all wanted a fun game, and the flavor I gave each mission was based on what they told me they wanted. At the end of each night, I would give them options for other sites to raid, plus one or two 'special mission options' (fuel convoy might be available but could be military convoy instead, rebels in the hills want to join but it could be a trap, etc.). Players picked their option, or struck out in a new direction for the next game, which I then wrote up for them for the next week.
This, to me, was the only way to keep the game from becoming a sanity-destroying monstrocity. It would be rediculous to write an entire world just for them to explore, especially with 95% never likely to be seen. Instead, focus on the broad strokes, then find what you need to fill in for each of those strokes.
For the simplest option, I'd suggest looking at Mech Attack. Very simple, fun, and a great set of easy but elegant rules. Not a lot of options as far as aircraft/artillery/space travel go, but most likely you can just wing something if it is important and go from there. I'd be happy to try to teach you Battletech if you'd like to try a game over Roll20 - I'm setting up a new campaign to run, and have a bunch of it set up already. I've actually modified BattleTech to run on a d10 system for my personal preference, but I can show you the proper 2d6 or both options if you'd like.