There are lots of ways to track campaigns.
Usually you'll want some type of map. Whether you use something like Planetary Empires or just a hand drawn map is up to you.
Depending on how complicated you want to get you can simply grant each player a total number of points to use throughout the campaign or get right down to named forces at the start. Simply doing total points is certainly the easiest to work with. For example, if it's a
40k campaign then having 5000 points total is a decent number. For every unit destroyed or that has more than 75% casualties, those points are lost. Named characters are an exception. If they are "killed" in the battle, then at the end the player gets to roll a dice. On a 3+ the player survived and can be used again. If the character is dead then it can't be used for the rest of the campaign.
You might get bonuses for holding certain points on the map. For example, the right to have an extra Heavy unit or maybe a point bonus (reinforcements) at the end of the round. I've heard that some people track Campaign Points
We tend to do 2 battles per person per round. So, that would be 4 battles per round for you. We also limit a single campaign to 3 rounds.
We also do a winner take all approach. Meaning, when a player attacks they indicate where they are attacking from and what place on the map they are attacking. Whoever wins gets both spots. This represents a player committing all of their forces from single map zone to take over another. We also have a rule that says you can only attack what is immediately next to your map point. Unless you have a starport which can hit anywhere on the planet(s).
If you are playing
40k, Crusade of Fire is a pretty good campaign. It builds on the Planet Strike box. For our latest campaign we have 9 planets with between 3 and 12 map locations each. Each planet has a certain feel to it (ie: Daemon World, Ice World, Tropical) with special rules that occur during the game. Most map locations have a special attribute like a shield generator or manufactorum that grants the controlling player certain in game bonuses.
Honestly, since we started doing campaigns we haven't looked back. It's one thing to kick your opponents butt in a single game; it's quite another to do several battles and throw them off of a planet..