The only 'critical' mod I can think of is the UOP, or http://www.nexusmods.com/oblivion/mods/5296/?. It fixes a lot of things in the vanilla game that Beth didn't get around to fixing. I'm not sure if this is the Official Patch you mention or not. Anyways, the most famous fix the UOP addresses is Callindil's shop in the Imperial City. It's called Mystic Emporium. Even though it's a shop, its doors remained locked at all times (I think) unless you pick the lock. And then, you'll get a guard yelling in your face! This is not supposed to happen, matter of fact it doesn't happen on PS3 at all, but on Xbox (and the vanilla PC game) it does. The UOP will fix this, though, among with dozens (hundreds?) of other things.
Every thing else is opinion. Other than the UOP, it's all opinion what is critical and what isn't. Everybody's got their own style.
And when modding, GO SLOW. Don't add a slew of mods (like 30 at once) and then try to play your game. If something is screwy (and chances are it will be) you won't know what is doing what. I literally add one mod at a time. I spent 5 solid years with the vanilla game, so by the time I started modding, I knew exactly what I wanted and what I didn't.
And by all means, If you have any questions, ask here, or PM one of us.