The most essential Skyrim mods are Unofficial Patches which will take care of all those bugs. The other one is Achievement Mod Enabler for obvious reasons.
Yeah it allows you to gain more magicka, stamina and health by killing and by getting hit. It is really good for a Berserker playthrough.
There is also another one I discovered the other day called Natural Growth and Decay, where your skills decay over time if you don't use them which makes constant training a must. I also love Disparity as it makes your character a truly unique one based on your style of play.
I came across another one called challenging spell learning which lets you perform a 10 second ritual and if you have enough magicka to cast the spell you will learn it but if you fail, your character will get debuffed. It really adds to the immersion.