Hey all!
I have been playing this game since it came out and I have learned some things based on my successes and failures. I'll list out a lot of things to do as well as things to not do.
Do: Arrange your shelter right off the bat in a strategic way. Raiders will come and you want there to be people who are well equipped in the first room with people in it. Sacrifice a few caps on removing rooms that are in bad places before building new rooms.
A good initial set up is:
Vault door - Barracks
Power Generator -Water Treatment
Med Bay - Food
This is because Power is the most important room and you should always have that room full. Equip these people with guns. I talk about this a little later.
Do: Complete as many objectives as possible very early.
Don't: Buy more of a room before upgrading your current rooms. Doing this makes it take longer to gain resources which will make your dwellers less happy.
D: Plan your vault layout ahead of time. Make sure things that don't produce something are placed where you can only fit 2 rooms across. The general rule is that each row can have 8 rooms and 2 elevators. as you can see, there can only be 2 rooms that can be expanded to 3.
Do: Rush often. it's not bad to Rush while it's under 35% but over that, you should be cautious. Rushing will also give you extra caps. so there is a lot of value in it. Just don't push it too much.
ALSO, SEE DON'T BELOW
DON'T: Rush a room that is not well equipped. If the room is 3 rooms merged, there will be 3x as many Rad roaches or Fires to put out. Do not rush rooms that are under staffed and/or under equipped. This can cause everyone to die, and you will most likely restart your game.
Do: Populate. Get people together and have babies. Increasing your population is key to getting on your feet. You need to unlock Med Bay as soon as possible to get Stimpacks rolling in.
Don't buy the Storage Room until you need it. It can take awhile for you to get enough stuff to store when you're equipping everyone with all the gear you get.
Do: Explore the wasteland. You need to do this only when you have a full supply of Stimpacks. You'll want to send 1 guy out with 15 Stimpacks and as many Rad-Aways and you can. This should last you about 12-16 hours. Make sure he has a gun.
Do: Give all your guys in the first room raiders would visit with people, ALL of your best guns and gear. This room should be a wall against raiders. Use Stimpacks to keep you're guys healthy.
Don't: Get the women in your defense room (the one the raiders will enter first) Pregnant. They will run away if there is danger in the room.
Do: Revive the dead. It's better that you keep your population high.
Don't: Play this game while paying more attention to something else. If the raiders come or the radroaches randomly attack when you aren't looking, you could loose a lot of people.
Time is still active while the game is off, but events will not happen. You won't loose all your energy/food/water while it's in sleep mode, only a little bit. But your guys who are in training will still level up their skills.
Do: Put as many guys in your training facilities as possible before you go to seep at night. Just be sure to put everyone back to work the next time you open the game.
Do: Train Charisma and unlock/upgrade the Radio Station. Bring in some new blood.
That's about it!
A quick note about buying lunchboxes. Should you purchase them, you should do so when you are built but suffering a bit. A few lunchboxes can go a long way. I spent $20 on 40 Lunchboxes a week after the game came out and it has proven to be very helpful. ( I've only used a quarter of them so far, not counting the ones I've earned)