You are going to be using different utilities for the most part. Wrye Bash is the most recommended mod manager for Oblivion. You will want BOSS for your load order and TES4Edit for cleaning mods. Some people also use OBMM instead of Wrye Bash, but at this point Wrye is updated more often and has a more powerful set of tools. You can still use OBMM as it is the easiest choice for managing .ini edits and shader mods, although you may not need to do either.
I wouldn't recommend using NMM for Oblivion because it was released quite recently, and the majority of mods on Tesnexus were never formatted for it, so there is pretty much a 50/50 chance of stuff actually working. This shouldn't be a problem (I hope) for Skyrim.
http://tescosi.com/wiki/Main_Page is the most up to date modding guide out there for Oblivion at the moment. Just about everything you will need to know is there.