Go up the Flamethrower line first, then the Acid Rifle line, and finally the Heavy Weapons Support line. Field Tactics will come as you get the others.
Get some Doc buffs (and Dancer/Musician buffs if you can find them) and head to the Tusken Fort on Tatooine or do Quenker missions on Dantooine.
Optional: Get some clothes with Bio-Engineer enhancements for Stun/Melee Defense. Be aware that the highest that this bonus can accumulate is +25 (even though it will add up higher, it will only count up to the +25).
Gained by killing MOBs with a Heavy Weapon.
Use a speed sliced Flamethrower to level. Only use the Acid Rifle when you absolutely have to, it sucks (atm).
Use Flame Single for a single target and Flame Cone for crowds. Remember that Flame DoTs no longer stack.
Combat XP is gained by killing MOBs by any means. It’s 10% of the weapons XP gained.
Commandos are unique in that they can gain 100% XP for Combat when doing damage with Grenades. However Grenades are slow, miss a lot, drain action fast, and cannot be used indoors. Besides, you should earn enough Combat XP as you go up the other 3 trees to advance in this line.
If you’re having problems raising it, remember that it’s a percentage of the XP gained for killing things. Just get some buffs and kill higher end MOBs. For example, Quenkers will give you around 300 Combat XP each!