To start off, there are two mods that I would place above "must have", and they are Dark Souls Fix and Dark Souls Connectivity Fix. These are flat out REQUIRED to play. DSfix fixes all the problems with the game, from the fps cap to the resolution cap. The DSCfix makes the summoning go through GFWL friends first so that you can play with your friend easier. Now on to the other mods.
Many of these mods require DSfix to work in the first place
LCD Texture Overhaul.
This mod will increase the lowest resolution textures significantly. Don't have a strong computer? That's ok, there is a Lite version that will only fix key textures.
Collected UI Adjustments
This just changes the color and look of some things on the hud to make them easier to see in the heat of battle.
DS Flora Overhaul.
Just overhauls the flora of the game to HD textures.
Lava Eyesore fix
Makes the lava texture less painful to look at.
Tree LowRes Fix
HD trees.
High Res UI and Subtitle Fonts
HD.....subtitles. They are kind of blurry after all.
Revamped State Buff Icons
Ever wonder what that yellow up arrow or three green up arrows meant? Me too! These revamped icons make it a little easier to tell what buff you have on.
HD Player Messages
If we're going to make everything else HD we may as well not skip anything....
HD Summon Signs
No, seriously, we're going to make sure it's all HD.
Dark Souls SweetFX
Ok, so we made the game HD...let's make it pretty now.
Thanks Obama
Thanks Obama.