Sounds like you want a fortress.
First, decide if it's to be ancient, modern, futuristic, or fantastic.
Ancient: A stone castle, with arrow slit windows, crenellations, towers, a portcullis and a dungeon for your foes. Good for knights and vampires, with only a slight change of decor. You can find several prefab castles on SL Exchange.
Modern: Quonset huts, utilitarian buildings and warehouses. Large fenced off areas to park tanks and helicopters and such. Missile batteries, and a high chainlink fence with warning signs and barbed wire at the top. Searchlights. Use lots of concrete and asphalt. I haven't seen any ready-made modern military bases, but you may be able to find some prefab buildings that will suit. If not, the construction of this style of building is very simple.
(alternative: A "rebel base" in an urban decay setting. Put your HQ in the sewers and venture forth to fight the Evil Corporate Overlords in their highrises. Well suited to a group of Neko.)
Futuristic: A space station, or a cluster of domes on the surface. Tall, spidery towers with no apparent purpose. There's a fantastic skybox near my sim of Lebettu that may give you some ideas. Just stroll down to our beach area and then fly up about 400 meters or so. Look for the domes with the propellers spinning underneath them. Some of the "space" sims also have great space station builds.
Fantastic: A series of caves under a volcano (there's actually a prefab for this one). A huge treehouse for the Elven King (Again, prefabs are your friend). Triton's underwater city of merfolk. A shimmery fairy castle in the clouds. A castle clinging impossibly to a cliffside.
I hope that gives you some ideas to spark your imagination. Thanks for the opportunity to get my brain started this morning, the caffeine hasn't kicked in yet.

[EDIT: The OP asked "how" to build a base, Lindal, not what sort of a base to build! Duh! The answer to that one is simple: One prim at a time. ]