Hey,
I hope this is the right place.
So I got this game with the humble indie bundle, which should be v24 if I'm not mistaken.
Campaign mode doesn't work yet, so I played some of the custom missions. There's one in particular, where you have limited resources and have to get a chip from out of a zombie cave. This was a lot of fun, I liked the whole reinforcement thing, and the controls are kind of awkwardly endearing as well.
But sadly, beyond that mission, I haven't found much to do.

Most other modes, it seems, are either made for multiplayer, or they require you to build a base and stuff each time, and then there's endless waves of enemies attacking. When I tried one of those, I figured I'd make myself a hideout that's as safe as possible, so I put it underground, surrounded by bunker walls. It turned out the AI wouldn't use the diggers to get rid of the walls. Also, you can place as many command brains as you like, is that intended?

I tried one of the user made missions I think, which was Tartarus, as it seemed to be very popular. It was a frenzy. Instead of limited ressources with which I could buy reinforcements, there was an endless stream of soldiers marching in on the battlefield all the time, making losing not an option. Maybe other user made missions aren't like that, so I think I'll try out a few more eventually.

How do you play the game? Is there anything obvious which I'm missing? Or more generally speaking: What parts/missions etc. do you find the most fun about the game?

First-party content is rather scarce at the moment, so it's basically what you make of it. You could mess around with weapons, or you could play some harder missions (weegee's are good if you're after a challenge) or you could play the defence modes and slaughter incoming enemies.
Also, placing multiple brains means you can lose some and still have some in reserve. This is intentional.

There seem to be two types of mods, additional guns and so on, and additional missions.
Right now I'm okay with the guns that are already in the game. I think the selection is pretty nice and I'm afraid that modded weapons might destroy game balance.

It would be cool to have some more missions like the one with the zombie cave. With limited ressources, where you have to figure out the best way to do things. I'll try Weegees missions I think. I failed a lot at the zombie mission at first, and it was still a lot of fun.

Oh, one thing that bothers me is, that even though you can save dropship loadouts, they don't transfer into the next mission. So all the time I have to set up the loadout again.
Also it'd be neat if you could just move things up and down in the loadout window. It seems that if you put in 2 characters and then 2 weapons, the lower character will begin with both of them in his inventory. To distribute them evenly you'll need to put in 1 character, 1 weapon, perhaps some other tools, then the other character and so on. I feel like that this process is more complicated and long winded than necessary. Perhaps it's on the to do list already...

Indeed they are really difficult, but quite enjoyable as well.

At this point the game is very much a sandbox, as in it is without very much structure. It is really up to you to supply structure in skirmish games. For example I often set rules for myself, like: Only use starting gold, make it so that I can walk from brain to the outside obstructed only by doors, and one brain. Its pretty fun trying to manage a slowly decomposing base with a shrinking supply of bodies.

I also like taking one brain unit and seeing how long I can survive. One Man Army is kind of easy right now. I usually start off with only a weak pistol so I have to scavenge right away.

If you're looking for more formalized play there are a number of fun missions. TLB's Prison Escape missions are great fun, and there's this one Assassination mission I had lots of fun with.

Really, I think you do 'get' the game, in its current vanilla state. There's just not a whole lot to do.
There are some great 3rd party missions, and some decent vanilla missions/game modes, but mostly it's just a sandbox.
But with mods, that sandbox has plenty of fun toys. And, well, I can't really think of how to extend the analogy to say this, but making mods for CC is also relatively easy.

Also, if you don't want to build a base or mine for funds you can always download pre-made bunkers and theres a couple mods that allow you to spawn funds like numguns AAL mod...and theres tons of maps and scenarios availiable and even a zombie survival mod if your into that.