If memory serves in the tabletop game there was a team based initiative rule, basically rolling to see who had to go first and then players alternated moving mechs. Also in tabletop it was clearly understood that heavy mechs were better but generally friendly games were done based on tonnage. So each team got 200-300 tons worth of mechs in their lance. That did create situations where people ran light or weaker medium mechs with their fourth slot just because of tonnage available left available. I’m not even going to talk about all the permutations on Battle Value as people tried to find more reasonable metrics than tonnage to balance out a match.
I feel like the initiative system in the Battletech video game is an improvement over tabletop but it’s aggravating in that it could be so much better with just a few tweaks.