There are certainly mods that can make Skyrim more challenging (like Frostfall) but will leave that area to others as it was never an issue for me.
I have about 84 mods, about 80% of them related to textures and graphics as I have been on a mission to make the game as realistic (in a fantasy type of way) as possible. Some are very specific - like moss on rocks (which is really well done), mushrooms, and ivy - while others tend to cover things like snow, roads, and mountains.
Some ideas:
W.A.T.E.R:
http://skyrim.nexusmods.com/mods/13268 and his (SparrowPrince) Moss on Rocks:
http://skyrim.nexusmods.com/mods/31856/
SMIM (Static Mesh Improvement MOD), pretty much a must have:
http://skyrim.nexusmods.com/mods/8655
Flora Overhaul by Vurt, another must have:
http://skyrim.nexusmods.com/mods/141
Armor by AmidianBornCabal - this person is pure magic in their armor textures:
http://skyrim.nexusmods.com/mods/24909
Immersive armors by Hotropper:
http://skyrim.nexusmods.com/mods/19733
Dramatic Clouds (unless you go with Climates of Tamriel):
http://skyrim.nexusmods.com/mods/4910
Climates of Tamriel - pretty awesome mod but I would wait as the author is about to come out with version3.0 with a very cool winter edition. Another genius mod:
http://skyrim.nexusmods.com/mods/17802
Sample winter edition, Riverwood:
Ruin Clutter is an awesome mod as well:
http://skyrim.nexusmods.com/mods/14227
Great snow mod:
http://skyrim.nexusmods.com/mods/28419 and goes well with Better Dynamic Snow:
http://skyrim.nexusmods.com/mods/10383
Visible Windows by Isoku (all their stuff is excellent):
http://skyrim.nexusmods.com/mods/6971
I also use a lot of enhanced city mods - if you are interested in any of those let me know. They really breath some live into the environment and can't recommend them enough. Most of the major holds are all done. Autumn of Whiterun is probably my favorite.
For characters … well that so depends on your taste. At the very least I highly recommend XCE - Xenius Character Enhancement. He did a great job at really refining and improving all the character textures while staying true to the theme of the game:
http://skyrim.nexusmods.com/mods/2356
Then smooth faces for ladies and gents:
http://skyrim.nexusmods.com/mods/1971
Now if you are looking for enhanced character graphics it depends on gender and whether you just want better faces or also better bodies. I use XCE for face, eyes, lips and warpaint and better males for the body. Here are some shots of my characters (below) and one of Aela the huntress to give you an idea.
Also I can't recommend ENB's enough. Super easy to use and change around they can change the look more than any mod on the net, especially combined with a good lighting mod like RLO, RS, RCRN, or ELFX. They tend to be very personal preference though depending how you feel about things like SSAO, DoF, realistic colors, cinematic, fantasy, etc. I happen to love Seasons of Skyrim and Project ENB by Bronze316. The Goddess ENB is also remarkable and well done. For a more realistic, and closer to vanilla, ENB try Skyrealism ENB. For an ultra intense bring your PC to its knees ENB, try K ENB.
Look through some of the images on the links below to get an idea of what can be done. K ENB is the current hot one.
Project:
http://skyrim.nexusmods.com/mods/20781
Seasons of Skyrim:
http://skyrim.nexusmods.com/mods/23812
K ENB:
http://skyrim.nexusmods.com/mods/30158/
The Goddess:
http://skyrim.nexusmods.com/mods/23029
Skyrealism:
http://skyrim.nexusmods.com/mods/23765
Aela with XCE:
My character, Grimolfr Nightblade:
Moon over Whiterun: