I'd clean with warm water (and leather cleaner if filthy!) then when it's dry I'd use a conditioner like Hamanol or Jeffries leather balsam. Personally I don't use oil any more, I prefer the finish you get with a cream and there seems to be some debate about oil actually damaging leather over time.
Ive just done mine
I picked it up today and asked as its so long since Ive had a new saddle. Mines an Albion with calfskin. She said not to use soap on the calf skin but to use the Albion balm and soap the rest and NOT to use oil. I looked on the Albion website and it says to use the balm all over before using it for the first time.