You might want to start out on an easier difficulty. The game basically tells you nothing about what anything does, so unless you're looking up a guide or asking Strife Werziel here, there isn't really a good way to know what research to get or how to optimally spend your money. I'm not even certain that a second base was worthwhile yet, although I imagine later on the rate of UFO landings will be high enough that the second base was required.
Also, we both use multiple saves and reload combat a fair amount. The one I reported where my whole team got bombed, I actually loaded a pre-landing save, which meant the entire terror battlefield was different when I tried the second time.