To just answer your question, focus on resources. Only build turrets if absolutely essential. Leveling up characters is the 'third' thing I worry about -- 1) surviving/establishing/industry focus, 2) science focus, then 3) food focus. More on this below.
1. Focus on upping resource production early on. In my opinion, if the first level crystal does not allow you to upgrade science, food, or industry (in order of my preference) just restart. Sometimes you'll get the opportunity to skip from lvl 1 to 3 for something like 65 crystals -- do it at all costs if you can - it saves you the cost of the level 2 machine, which is huge early on.
2. On level 1, first build a industry generator. Then science. Then food. You'll need the industry to build other generators. You'll need the science to buy upgrades and ensure you get enough for the artifact upgrade (46 or 65 science, depending). Food is for leveling up, but I don't worry about too much - though if you have a character with the 'Operator' skill at level 3, I level him up to 3 asap (usually at the end of level 1) before worrying about my door opener/combat unit. I generally keep this the order until I feel safe enough to focus production (discussed later).
3. Operators take 1 turn to get ready, then up production. So... put them in a choke point and never move them, preferably after you open your first door in a given level.
4. Later on, floors get huge. In my opinion, you should open in one direction only from your starting block, until you have both: 1) a defensible position, and 2) enough dust to power a room. Now, you can open another direction from your starting point with your warrior, and power the room so you don't get attacked from behind your front line. Now go back and open more doors on the 'defended' corridor, until you earn enough dust to power a room -- go back to the other non-defended corridor (or another door connected to base), open and power. This way you can keep pushing forward - you never want to open a door next to your crystal without power to light the room. Once you exhaust rooms in your defended corridor, you have also lit up some rooms in other directions that you can now add defenses to, and all giant 'mobs' from unlit rooms will spawn into the first killzone and be torn apart w/o much supervision.
5. By killzone, I mean unmanned rooms... preferably long ones with 4 or so minor modules. For levels under 8 or 9, one or two rooms with 2 Neurostuns (slow enemies) and two Tear Gas should rip apart almost anything. In my opinion, beyond resource production Neurostuns are the most important -- they bring enemies to a crawl, giving both time to react to other situations as well as damaging them tons with minors in the same room.
6. Eventually you'll find you need to also defend rooms. Dust Field Gens (2 stacked) give a huge boost to your defense (and thus life). Tear Gas does over time damage, but more importantly lowers enemy defense. So two of them would be nice -- later on replace one with a KIP maybe, if you have the science to max it out.
7. No matter how well prepared you are, later levels are HARD. Even outlets for major modules are rare, meaning it's hard to produce anything even with your crazy level 4 science thing since you have nowhere to put it. Dust is also rare, meaning it's hard to set up defenses.
8. Keep in mind pricing. If you're going to level up your science generator for 100 science, be sure you think you'll actually earn more than 100 in the long run. Looking back, I'm not sure if the ones that cost 100 are ever worth it unless you luck into a huge level that is set up really nice for massive production.
9. Minors I love: Neurostun (essential), Dust Field Gens, Tear gas, Kip. You may find success with others, but that is a focused set that buffs your defense, debuffs theirs, and does serious damage in both manned and unmanned rooms. (obviously no need for DFGs in unmanned killzone rooms.
10. Early on, try to leave a level with at least 20-50 industry so you can start building right away. On level 1, I only build prisoner prods if I absolutely have to. On level 2, you'll probably have to, but still try to save as much as you can. Later you'll want at least 100 so you can also build minors right away.
11. Starting level 2, I really try to focus on science. You can often find 1-3 artifacts on any given floor, so with tons of science and a bit of luck finding them early, you can build a pile of upgrades on a single level by having all 3 producing at the same time -- and remember, opening the last door will finish all currently making something. Excess science will fuel your KIP one you research that (it doesn't use it up, just powers it) so it's never a bad thing.
12. Once I have a nice swell of science, on a later level I switch over to heavy food production. We're talking it's the absolute main focus -- (once you're in late levels it's hard to produce anything). Once I have everyone to level 7 or 8, I focused on getting my door opener to level 15. Scamper is an awesome door opener skill for getting through 5 unlit rooms back to your defenses, though I beat the game without it.
13. At some point, it's in your best interest to stop looking at the combat on screen, and instead look at your 4 character panel up in the top right. This way you'll see everyone taking damage at the same time, and won't miss some mob spawn killing some character you weren't focusing on.
14. On later levels (9-12) you may find yourself unable to light rooms or build production. Find the exit, cross your fingers, and run. I had to do this twice to win. I'm sure with luckier runs I'd have been able to get more out of those levels, but you need to know when to cut and run.
15. Shops are expensive. Only buy the best stuff if you really need it and the cost doesn't wreck your build plans.
16. Character death isn't the end. I lost 2 on my winning run, including one I'd invested a lot into (stupid death too, he earned stuff for enemy kills so I moved him into a killzone room with lots of almost dead enemies and they tore him to pieces before I could evac or heal him.. insta death).
17. I won with one door opener, and 3 operators. The operators just needed to operate and survive, so I amped their defense with minors where necessary, and used my door opener and killzone rooms to survive. My door opener would often have to run from combat zone to combat zone, saving the day, while my ops all stayed still. A good operator also has buff skills - armchair general or paramedic are nice. The chef has an amazing Damage over Time for all enemies on floor too.
18. There are very, very, very mean monsters later on. I'll leave you to discover them.
19. You'll want around 30 food in reserve on level 2+ to recruit. I spend my first food on leveling up an operator, then save food till I can hire. I'm not usually focusing on food production at this point, just ensuring I can make an operator and hire.
