In order to reach level 30, you need to get 423700xp. This could take around 150-200 hrs of playtime (see comments for explanation).
You get xp from completing coop missions or verses matches.
Versus matches can reward up to 500xp in the Storm game mode. Other game types only give you 400xp max.
The problem is that only the top players get those maximum rewards and the others get substantially less. So this game is not boost friendly in this regard.
You do not get xp for each kill, but rather your xp reward is based on your point rank for that match.
This solution is a work in progress and I am checking various scenarios. If you want to experiment with boosting Versus, here a couple things I have noticed from my experience so far.
The number of people you have is one of the factors that dictates how much xp you get. (I think you can max out your reward with 8 people. I am still working on getting a full 16 player lobby together to test this out.)
The other thing I discovered is that if you tie for first place, it counts as first place (see my solution for Top Dog). This means that there is a possibility that everyone could get the same maximum xp reward.
Then there are coop missions. One great thing about this is that all 5 squad members get rewarded the same amount of xp. You can get up to 1800 xp from a single hardcore coop mission, but I would recommend this if you were a dev and had unlimited revive tokens. (Unless you can find a HC mission that you can work yourself up to do quickly, see comments) But if you are like me, just doing one speed run each day of Regular and Skilled is the way to go since it is the most xp/minute thanks to the one time per day daily bonus.
For this I recommend a squad made up of 4 medics and 1 engineer (all with speed boots on if available).
This of course depends on the mission (I will try to add mission specific recommendations later) but this is generally a good setup if you are just trying to quickly finish the mission and get your xp.
When it comes to time, one of the most time consuming things can be the heavy gunners. The quickest way I have found to do this is to have one medic act as bait for the HG while healing themselves. You should have another medic or an engineer help them out with this by standing behind "the bait". Then the other medics just keep using the defibrillators on the HG's backpack (aim right in the center of the light on it). You'll be finished in seconds since he doesn't move around.
For Skilled you'll want to have a medic AND an engineer healing/armoring "the bait".
One more thing on coop is that each mission gives you some "Commander's Orders" which you can see listed in your stats when you press the back button. They will be something like "Defibrillate 6 Enemies" or "Get 10 Kills in Slide". This allegedly can give you 10% more xp but I have only ever gotten a maximum of 9% more xp from doing this. It isn't too bad on the Normal missions, but I hardly ever bother on Skilled or Hardcore. But keep an eye out for this little bonus.
You also can purchase boosters to maximize your efforts.
Also this is so far just speculation, but do not rule out the possibility of future 2x xp events or discounts on boosters. These freemium games often do such things. It is just something to consider/look forward to/pray for. And note that boosters work on all xp earned in-game including coop first-time bonuses.
Coop Path B - 120 (+0)
Coop Path A - 132 (+0)
Coop Regular - 264 (+216)
Coop Skilled - 448 (+280)
Coop Hardcore - 1260 (+540)
Note that the first time you complete a mission each day you get an xp bonus. I indicate that above in parentheses.
List of Ranks:
[Sources/Related in comments]