To start out with, I'm a big fan of complex, mechanism mods. I also like adventure mods, but I go towards mechanism mods first. I'll list some of my favorites and why I like them:
UI mods
1. Inventory Tweaks - This allows you to short your inventory with a keystroke, and press a button to short a chest. This is *very* useful as you start adding mods.
2. WAILA - What Am I Looking At is a mod that adds a little window that pops-up whenever you put the cross-hair over something to something to interact with it. It tells you what that object is and what mod it came from.
3. NEI - Not Enough Items - Note that this mod has a cheat mode, which lets you control several aspects of the game even in Survival mode. In its recipe mode, however, you can easily find out how to make almost anything registered to it. This is very useful when you start adding complicated machine mods.
4. Zan's Minimap - Its a map. That's always useful. In addition to seeing your local area, however, you can also see a map of anywhere you've ever been on your world. You could get Rei's mini-map instead, which drops the exploration map for a mob locator.
--
Machine mods:
1. BuildCraft - This mod adds a number of machines. I like it for the Quarry and the Filler.
2. IndustrailCraft 2 - The granddaddy of all mods. This mod adds many complex machines, but thanks to a newer competing mod there isn't much point to it until the endgame where its modified machines are faster than its competitors.
3. Thermal Expansion - This is IC2's rival. Pretty much anything IC2 Thermal Exapnsion can do too, frequently more easily. With this mod you can teleport power, items, and or fluids around the map, double your ore output, and
4. Applied Energistics - Applied Energistics (AE) is known for two things. One, it has one of the best auto-crafting systems available in mods. Two, It has one of the best compact storage systems available in mods. These two things alone make AE a great system when you are using other mods to gather massive amounts of material. (Note that this mod must be powered, and does not have a means to generate power on its own.)
--
Utility Mods:
1. Tinkers Construct - This mod allows you to make custom tools and weapons, and then enchant those tools with material instead of levels.
2. Extra Utilities - A number of separate blocks that are just plain useful. Includes the Ender Pump and Ender Quarry, which are low-impact versions of the items in BuildCraft.
3. Open Blocks - Another collection of useful utility blocks.
4. Better Chests - Adds multiple levels of chests which can store so much more than the lower tiers.
5. JABBA - This is one of the best barrel mods currently out. A barrel is a block that can hold huge quantities of a single kind of block, like 64 stacks of cobblestone your quarry digs up.
--
Magic Mods
1. Thaumcraft - This mod creates magic by drawing it from existing objects. A very complete and useful mod.
2. Ars Magica 2 - This mod draws magic from you, and allows the creation of custom spells.
--
Adventure modifiers:
1. Better Dungeons - This mod adds several new mobs and *huge* dungeons full of dangers and loot to explore.
2. Infernal Mobs - Have you ever played Diablo or one of its clones? If you have you will have run into monsters that are modified with keywords that make the monster more powerful. This mod adds this to Minecraft. A Spider is bad. A Firey Teleporting Slowing Spawing Spider is *much* worse.
3. Mystcraft - Are the three worlds of the Overworld, Nether, and End not enough for you? Then take this mod and make limitless additional worlds to explore! Just make sure you take a Linkbook home with you, or be prepared to be trapped forever.