When you have a lot more mutants than your previous playthrough, use the red button and start over. You will receive a large bonus from the mutants that you have. This will allow you to progress a lot faster after each reset, as long as this is done with more mutants present than your last playthrough.
Humans
Humans are used to get bonuses after each new Doomsday that is triggered. They are obtained by unlocking new rooms.
Money
Build rooms in your bunker to earn money. You can then upgrade them to make more money and build new rooms. Because upgrading costs quite a bit, at the start concentrate on unlocking all the rooms first, then upgrade them later to get extra stars. You usually have get a room to level 25 before unlocking the next room, however this will eventually change with mutant bonuses. Get as many rooms as possible to level 25 (and earn the first star), then work on the more expensive ones at the same time as you progress with the cheap rooms to get them to level 50.
Mutants
New mutants are obtained by tapping the animals at the top level. Note: You will also get money by doing this. Your bonuses will increase as you play.
Perks
Early room perks are not very useful. Do not bother with them until you have all or most of the rooms at level 25. As the levels of your rooms increase, the bonuses conveyed from the perks become larger. Begin constantly investing in perks to take advantage. Consider purchasing a few perks each time you resume the game after a significant break, then spend all your remaining money on upgrading rooms.
Wheel bonus
You can spin the wheel occasionally to get a bonus to your profits. This is done by watching an advertising video. Do this whenever possible to maximize your profits. Have the bonuses active when you are not logged into the game to keep up your profits.