Base

The base is made up of rooms, corridors and traps. In addition, you can also build buildings outside of the "base", like Top Side shacks and Hotels.

Entrances

I tried experimenting with multiple entrances to make getting to the Depots easier, but found it wasn't worth the hassle of having a secondary way for agents to get into my base. The two hallways you see there are for dual purposes. Agents and minions seem to want to go the shortest route into the base, Place only low HEAT items near the entrance as investigaters often get bored and just go home.

Second Island

First off, don't have your full compliment of minions when you move to the second island, I usually move with 96 or so. Second, don't collect all the items from missions you can - I just tend to get the 5 uber-loots, mirror, cloth, totem pole, and the sound thingie from Russia - basically any loot that can be researched. I also try to demolish my old base as much as possible - you get money back.