Firstly decide on when/where your character was born - this will have a profound effect on him/her. (eg. An 18th C. Dandy of the Parisienne Court will have a completely different idea of the needs of business to an 80's Wall Street financier.)
What was his/her mortal life like? Did you start off well off or poor? How did you get noticed? Did you have to work or have you always had everything handed to you? Does (s)he still have an accent? - How noticable is it?
Do you have any living Mortal relatives? Do they know you? Who are they? What sort of contact do you have with them? (Are you a sort of Guardian Angel, or just "cousin John - you know - the wierd one"?) What about friends?
What was your Mortal occupation? Were you the recognised leader, or did you rule from the shadows? Was your job the reason for you being chosen for the Embrace?
How did you meet your sire? What drew him/her to you? Did you serve as a mortal or ghoul first? Were you given a choice? How was it done? After your Embrace how was your reaction to the world (sights, smells, sounds etc...) What was your first feeding like?
How much of Kindred ways did your Sire tell you? (eg. Traditions, Clans, Camarilla/Sabbat, History etc...) How did you manage to fit into your new role? What was it like to reach the top of the heap, only to find out that it reached the bottom of the ladder?
Does your character have any info on other Supernaturals? (Changelings, Garou, Mages, Mummies etc...) How did you get it? Have you met any?
What is your relationship with your Sire like? Are they still around? How much of his values did he impart to you? Does she have sway over you? Have you taken the Blood Oath? Did she ever Condition you? If things are not amicable, how much has he done in the past to stop you? Is it dislike, or hate? Did/does she have a reputation - good or bad? - that may affect you? Have an idea of your lineage...
What are your opinions of other clans? How have you reached them? Are these flexible opinions or are you very set in your ways? Do you have a reputation, good or bad, with another clan? Do you know any of the kindred in the Fief already? How? Where from? Is it a friendly relationship, or not?
What are your political leanings? (Are you traditional, an Anarch, or Sabbat maybe?) Are you a staunch supporter of the Camarilla?
What is your standing in society? Are you known in Vampire society? Is this because of something that you have done? Who you are? Who you know? Do you have friends in high places, or low ones? Do you have some blackmail material over an Elder who you are forcing to give you a leg up?
Night to Night Living
How do you spend your spare time? Do you have any? What social circles do you move in? What is your haven? Is it safe? What sort of security do you have? Do you have more than one haven? Do you have a right of Domain - Where?
How do you hunt? - are you seen at select nightspots, the local "Rack", or just off the street? Do you have any disturbing practices when you feed? What is your feeding restriction? Do you have a herd? Retainers? What do they know about you? What do they think about your "quirks"? Have you ever had a run-in with the Law? How did that go? Do you have any hunting grounds?
How do you travel? Do you have a car, van etc..? Can you drive - or do you have a driver? Does it have any special "custom modifications"? How do you get clothes etc... when the shops are closed at night? How do people get in touch with you?