Here are some of the ones I use that I consider essential to a more "immersive" Skyrim (and a couple to improve the UI). And if you haven't installed Nexus mod manager to manage/install/remove mods, you definitely should. It will make the process of maintaining your mods infinitely easier! Nexus Mod Manager

Visuals:

WATER: Water and Terrain Enhancement

Lush Grass: better grass in envrionemnt

Lush Trees: better trees in environment

Realistic Lighting with Customization: So far my favorite lighting mod, as title says lots of customization

IMAGINATOR: Allows you to adjust brigtness, contrast, saturation, tiny among other things from an in game spell. Also has some great presets for you to play around. Very flexible mod.

Crimson Tide: Very cool blood mod! Not really "essential" but I liked it so much that I can no longer play without it.

Sounds:

Sounds of Skyrim: The Wilds: Ambient noises of the wild, great for immersion

Sounds of Skyrim: The Dungeons: Ambient noises for dungeons, this mod is absolutely fantastic! It really gets me in the mood of the dungeon.

Sounds of Nature: Fire: Better fire sounds. Sound clips are on a much longer loop than vanilla sound so you're less likely to hear the same fire noises over and over, higher bit rate and taken from recordings of real fire.

Sounds of Nature: Water: Same as the previous mod, just with water instead of fire.

UI: A Quality World Map With Roads: Addition to the world map that shows all roads, can be customized to either show ALL roads or only main roads.

SkyUI: Probably my biggest issue with the vanilla release of the PC version was that the menu was directly ported over from console. The vanilla menu caters to the dpad of an xbox/ps3 controller. This menu overhaul is an ABSOLUTE must for any PC player.

Those are my recommendations, I'm sure there are some I've missed that others consider essential, but its a start for you!