I've been using the Skyim HD 2K textures. I only have 1GB of VRAM and it runs fine. Some other mods I think are well worth it:
Skyrim Mesh Improvement Mod - Updates a lot of meshes to make them look way better. Things like chain links and ropes now actually have 3 dimensions rather than 2. Improves lots of furniture pieces.
Skyrim Script Extender - Required for a lot of mods to run.
SkyUI - The default interface is ATROCIOUS. As in how the hell did Bethesda think that the way to view inventory items they gave us was acceptable for an RPG? This fixes that. Also introduces the MCM menu which lets you configure other mods a lot easier.
Unofficial Patches - There's an unofficial patch for Skyrim and each DLC that contains bug fixes.
Those are the ones that I consider mandatory. From there you can delve into all sorts of things like lighting enhancements (Ultra Realistic World Lighting, Real Lighting Overhaul, Enhanced Light and FX), water enhancements (Pure Water or WATER), immersion mods (Wet and Cold, Winter is Coming, Frostfall, Splash of Rain, Immersive Weapons, Footprints) and ways to improve gameplay (Convenient Horses).
all of these. I've only ever used SKyrim HD with most of the additional meshes mentioned here. It works great (also on only 1gb VRAM).
Also, you can't really play Skyrim without SKyUI, imo. It is the single most important mod for PC. As mentioned, you first have to install SKSE, and for many of these mods to work fully, you just have to load the game through SKSE, instead of through steam. Some have particular install processes and load orders that you need to fiddle with to make sure there are no conflicts--make sure the patches and Skyrim HD are near the top, with the various other meshes and re-textures installed and loading after HD (or the official texture pack, if you prefer). There is also one that simply improves the Linen textures. I find this to be very useful, because so much of the dungeon environment is covered with linens, and the base texture is pretty terrible, and Skyrim HD doesn't do much for this. It also effects the various flags you will find throughout.
Added to the Immersion mods, You should get Climates of Skyrim and Sounds of Skyrim.
Frostfall & Wet and Cold add another dimension to the game that really should have been an official part of the game. It seems a bit complex at first, and maybe annoying, and while it has seemingly no impact in parts of the map (the beginning areas), it drastically alters the way you plan your travels to certain parts of the world--head far enough north, get caught in a blizzard, and you will die in minutes if you don't have the provisions to get to your destination and back. Cloaks of Skyrim also works well with these two, but it does add more clutter to the world, if you find that to be a problem.
I'll also recommend UFO, or Ultimate Follower Overhaul. This has a bit of a complex install protocol, so be sure to read all the notes before installing it. It allows better management of your followers, and even grouping. (though more than one follower is generally OP). Also adds functions for horse control and allows followers to get their own horses.