I know there are a lot of ways to handle unit activation and the turn order ('Mech by 'Mech, lance by lance, using a deck of cards etc.). With Alpha Strike, I've gone one step more simple... alternating units, but when you activate a unit, you resolve all movement, attacks and damage for that unit before going on to the next unit. So I will move, shoot and resolve damage for one 'Mech, and then my opponent will do the same (and so on until all units have activated).
Pretty heretical, considering how much "simultaneous damage" is a sacred cow for Battletech, but it works great! It really balances the pros and cons of going first... yes, you play your hand and open yourself up to being outmaneuvered and flanked, but you get to choose when and where your attack falls (possibly taking out an enemy before they can strike back). It also really encourages units to get "stuck in" instead of playing the dance of "should I commit or not?" Instead of dancing around the margins of the battlefield, you see 'Mechs charging in and getting dirty.
Does anyone else play like that?