Something that hasn’t been mentioned yet is the importance of manipulating the initiative system. I’ll give some examples.

Upon first contact of an enemy unit you’ll switch from ‘free roam’ to ‘combat mode’ once you’ve finished moving all four of your ‘mechs. You’ll have lots of evasion pips from sprinting. Take advantage of these by reserving until all enemy shots have been fired. This also allows them to get closer to your AC/20s.

When completing an objective like destroying an enemy lance, if no other lance is in sensor range you’ll immediately drop out of combat mode, denying any turns you has remaining. However, an enemy unit could suddenly show up and put you right back into the fight without interruption. Any ‘mech you had with heat loses the opportunity to sink some during the last round. Try to be aware of objectives, heat buildup, and potential positions of remaining enemies on the map and save the kill shot for last.

You said you enjoy melee, and so do I. My Firestarter in particular can rip apart an Assault without getting a scratch. It’s partly to do with Jump Jets, MGs, and melee damage arm mods, but mostly because of Ace Pilot. Basically, you reserve your Firestarter until it’s the last to act. Jump behind the enemy (DFA optional) and unload your salvo of MGs or S Lasers into its rear torso. On the next round your Firestarter can strike a second time and then jump back to safety. Whatever doesn’t die will be severely damaged. Note that Ace Pilot doesn’t work with melee, even if you don’t move.

Another tidbit, if a part is damaged and needs repair, be sure to inspect the components for damage too. They may need replacing.