The dual time at first could be towards a high performance/high altitude endorsement, type specific towards BE20, or towards an ATP. Obviously you can't log PIC time without the hp/ha endorsement - and as a rule of thumb, the first PIC time you have should be type specific training as dual, even if it is just a Part 91.
There is a book, "Everything Explained for the Professional Pilot", that explains this and just about every issue similar from the FAA's point of view. It is a great book for getting a real interpretation of pretty much all of the regs. I'd be a little careful logging "SIC" in a aircraft that doesn't require a type rating, unless the two pilot thing is on the OPSPEC. Also, if you do log time in the BE20, be prepared to answer very system specific questions on an interview.