So as others have said: max out your brainers asap. More brainers mean better stuff, better stuff means fewer deaths, fewer deaths mean better, more experienced hands.
For a lot of the stuff you'll want better manufacturing as well, the main base can't house enough runts, if you also want all the neccessary research buildings and those sweet medic buildings (most of which have brainer space as well) that you'll want to get your gals back on their feet quickly.
If you sell your starting 5 hellerium (you can produce more), and any non-stunning weapons (keep bats and handles, sell early-game swords - you'll have better ones before you need them), you should get 1 brainer very early January. I can usually get 2 more at the start of February if I've been doing well in easy missions, then about 2/month after that. They're expensive, but they also get you points, which increases your long-term income. You'll need a second prison pretty early, but ransoming common enemies (tough guys/gals, church neophytes, nurses, etc.) is fine and profitable.
Take every "save a sister" mission you find (extra gals), probably every temple raid (easy when you know where enemies will be), and dark sacrifice (poorly-armed enemies with interesting loot and sometimes a gal). If they're too tough, run (take what you can). I think your gals only gain stats when they've knocked out or killed an enemy (not friendlies), so doing every mission you can with 5 or 6 gals (early game) is important. Pogroms aren't too bad, because the mutants can fight, but don't take them on until you're sure you can fight. And more difficult enemies have better loot/knowledge to interrogate them for.
If base defense missions are difficult, try to put all of your burrows (and the upgraded animal pens) and barracks (and upgrades) right next to your hangars and airlock. Those are the only places gals spawn, and hangars/airlock are the only places enemies spawn. You don't want half of your people on the other side of the base and half fighting.
But most of the difficulty seems to be related to time. There's the easy base defense against nurses and drones now in March-April, Doom Guys (from the video game) start showing up after a while, then mercenaries (mutons), bases, star gods...
Also, try to build/hire on the first of the month, or close to it. You pay upkeep for the entire month, even if you don't have use of the people/building until the next month.