Hmm I'm sure others can give you more useful tips but my favourite one is: if you are reloading/if you have no gun, and you are close to your enemy, just crush them into the ground (while jet-packing, if you are facing the right angle).
As for campaign mode.. You send money to a location every turn with the option to also scan, used for the fog of war. If the enemy also happens to send money to the same location then you will enter a battle, otherwise you will take it over the next turn. If you've taken over an area you can build a base (I have no idea how auto build works for the player) once you're done, the next time the enemy attacks that area, you will be able to defend your brain and troops better. I think thats about it... If you notice the enemy has 0 brains and you havent won, then you bugged out. Otherwise have fun!
EDIT: Old thread on tips for CC (I was looking for a different thread but I've seen this one before too):
viewtopic.php?f=4&t=21036