Base Layout Strategy
At higher difficulty levels, alien retaliation can often come MUCH sooner than you might be ready for-- before you have base defenses built, and before you have powerful weapons to arm your troops with. Considering that the access lift and all hangars serve as entry points for the invaders, the starter base has all the defensive virtues of a screen door:
The hangars and lift are distributed as widely as possible through the base, giving the aliens a wealth of breech points and enabling them to assault any defenders from all sides.
With this in mind, I recommend a partial rebuild of your initial base ASAP. Build two hangars next to the topmost hangar to replace the lower two, and a living quarters down between the two lower existing hangars to replace the one next to the access lift. Place any other new modules on the lower half of the screen, where they will not touch the lift or the new hangars.
As the new living quarters and hangar are completed, dismantle the old ones. It should now look something like:
Of course, any other new facilities with a mind to preserving the new choke-point at the grav lift (i.e., nothing adjacent to the top hangars.) This layout isn't as fortified as many new-build bases can be, but it's a good compromise between defendability (one choke-point at the lift), available space, expedience (it converts from the standard layout in minimal time), and, especially, cost. It only costs the price of two hangars and a living quarters ($800,000) to overhaul your base this way-- a cost that can be covered by the proceeds from, say, one small landed UFO.