XP32 Maximum Skeleton Extended [is pretty much a requirement for any animation mods. RaceMenu [gives character customization options similar to oblivion's and much, much more. Basically you can configure a mod's features in-game. The following mod is SkyUI [Not only does it make the interface better looking and more intuitive, but it also has the Mod Configuration Menu which tons of mods make use of.
It's a must-have even if you wanna play vanilla Skyrim. Unofficial Skyrim Legendary Edition Patch [fixes most if not all of the game's bugs. You can watch MxR's video which goes more into detail. Next up, the modding tool I recommend is Mod Organizer [It has tons of nice features which most if not all other mod organizers don't have. I dont need to go into detail about what it does. It's pretty much a requirement for tons of mods. In this section Ill be talking about some basic mods which everyone should have on their Skyrim installation when they start modding.