I just completed the main story of the original untouched game, and now I want to roll a new character and play using the best mods available.

I haven't even looked at the mod forums until now, so lets get some posts up and get all the good mods listed in once place.

No More Blocky Faces
Glowing Ore Veins

Easily the two best existing mods (outside stuff that accesses RAM).

"best mods" is subjective, the mods I like, you'd probably hate.
You're better of picking them yourself.

skyrimnexus.com click on "Top 100" and also use search, or actually better is to click on Categories, and pick the categories of mods you're interested in.

That's how I do my 'mod shopping', because everybody has different tastes.