my 2 cents
Having experience is exactly the kind of ops you are planning for the past 10+ years on both sides of the isle I wonder why you are not considering using some management company (TAG, Jetaviation, Globaljet etc etc etc) rather then reinventing the wheel all over again.
However, if you are going at it alone please consider the following:
Crewing: 4 pilots/aircraft - this offers the flexibility you need to allow for training, leave, sectors requiring augmented crew. The rostering schedule depends on where the crew will be based. If you allow crew to live away from your home base (i.e. anywhere within continental Europe) then a 14/14 rotation is what most prefer. This translates into 15 duty days (2 in transit) and 13 days off.
Type ratings: This depends on how you plan to operate. If your company plans to apply for an AOC you need to adhere to EU-OPS 1 and as a result will spend a lot of time and resources to all kinds of courses and training. Having dual ratings is not recommended in that case. In the latest iteration (of EU law) there are severe restrictions on cross training and operations.
Operation type: "private" - good choice. This gives you some freedom of overly restrictive OPS 1 , FCL and 145 issues. In my opinion these are made for airlines with far greater recourses don't cater for the specific difficulties of corporate operations. Some corporate flight departments use EU OPS as a guideline and use their good judgement as to when to abide by it and when to deviate.
Command structure: Cost wise 2 captains / 2F.O's per aircraft. But there is no reason why 2 captains can't fly together if you choose some other structure. Any crewman with a modern western training and attitude should be able to work with anybody with the same.
I would be happy to provide more "insights" if you want. Feel free to PM me.