I have introduced a couple of people to Battletech classic over the past year, with myself being fairly new to the game, so from my perspective:
1v1 is good for learning the basic operation but will devolve into a 4-6 hex standoff blasting away, not a lot of tactics coming into play but allows people get to grips with basic movement, heat, weapon cycling etc. Doesn't excite me and doesn't show off Battletech in its best form but good for fundamentals.
2v2 takes everything from 1v1 but brings movement, flanking and other tactics into play. Much more interesting and starts to get into what makes Battletech fun, if they aren't completely green this I think is a good starting point.
I would stick to 1 medium and 1 heavy, as the tactics are kept simpler and similar, lights and assaults require a different thought process to get the most from them, so best left until people are more comfortable with the game.
4v4 when players are comfortable. 2v2 can take a few games, I haven't introduced objectives even in first 4v4 game as there is still a lot of learning being done, and this is where assaults and lights can be introduced. I would ideally set the 'mechs to be used before allowing your players to select from a range of 'mechs as they develop a preferred style of play.
I think your plan for the first game is good, I think your second game you are trying to introduce a little too much in one jump. But that will come down to how well people latch on during the first game and are ready for that complexity. I have taught green people to board games in general, so my path is slower than if my friends were more used to board games.