the only problem I have with this mode is the idiotic speed that disasters spread. A lunchbox gave me ONE "rare" dweller which was level 10 with 1endurance (so barely useful). I noticed that the best strategy early on is just reproduce until you have a medbay, create rooms that are only 2 spaces and NOT upgrade them, have the living quarters only 1 room (and fully upgraded). Then... just be patient. Stock up on stimpacks at the beginning. Once you have roughly 10-15, send out ONE dweller with 2 or ideally 3 Endurance. Do not reproduce, stay at the level of dwellers you have when you unlock the medbay (16 I think?). Be patient, and bring back your one dweller with whatever loot he or she brings back. Its slow, but steady. Equip your dwellers with whatever he finds, and make sure to get early objectives when possible. I was not so lucky, having 4 lunchboxes without any rare weapons, armor, or anything moderately useful save for one Dweller (who frankly was not useful or special).
The biggest problems I can see people get with this game are;
upgrading rooms
sending out too many dwellers at once
procreating constantly
Seriously, you need to take survival mode SLOWLY and adapt to the difficulty. The high resource consumption by dwellers and disasters can easily overwhelm you.
Even in the normal game, a group of deathclaws bring my lv50, 10(+3)Endurance dwellers down to 30-50% health. And those are dwellers trained in E at level 1, and leveled after that. I shudder to think what they would do to a vault of level 18 dwellers. Eat them I suppose