While we're learning biology, let's learn some programming too! ComputerCraft adds programmable computers and turtles into Minecraft, which you can write code to control. It's based on the easy-to-learn Lua programming language, and with it you can make passworded doors, private chatrooms, automated mining turtles, and even in-game videogames. The possibilities are endless. Grab it here.
Thermal Expansion 4 & Minefactory Reloaded
These titans are two of the most important technology mods in the game. Thermal Expansion focuses on power generation and storage, as well as adding a bunch of new metals that have become standard components of several other mods. Minefactory Reloaded is where you're going to use that power—in automating farming, animal husbandry, mining, enchanting, potion-brewing and more. Install it for the 'raw meat block' alone. Grab both mods, and a couple of extras that they need to run, here.
After a while with lots of tech mods installed, you'll find that your power needs are growing faster than you can add more generator capacity. Big Reactors is the answer. It lets you build highly-configurable customised nuclear reactors that output huge amounts of power and won't melt down spectacularly if things go wrong. It even interfaces with ComputerCraft, so you can build programs to control your reactors. Budding nuclear engineers can grab it here.
Chisel & Carpenter's Blocks
Making your base pretty is an afterthought to some players, but to others it's a vital part of the game. These two mods give you the tools you need to customise almost every aspect of your base design. Chisel provides loads of new texture options for many of the most common blocks in the game, while Carpenter's Blocks adds slopes and loads of aesthetic options for doors, switches, torches, ladders, fences and more. Grab them here and here, respectively.
RailCraft & Steve's Carts 2
You can probably guess what these mods do. That's right—they both substantially upgrade the capabilities of Minecraft's minecarts. RailCraft adds a bunch of new types of track, including sophisticated redstone-controlled junctions and signals, while Steve's Carts pumps up the capabilities of the carts themselves—adding brakes, shields, drills and more. You can even make an attachment that launches fireworks. Grab RailCraft here, and Steve's Carts 2 here.