I don't work for NJA, but my understanding is that interviews get scheduled roughly one to two weeks from them receiving the application packet (at least that's what it was this summer), assuming that everything is in order. Interview process is two day, they fly you out and put you up in a hotel while you are in CMH. The interview includes a tour of the facilities and the actual interview process, including a sim ride.
You can be placed into any of the fleets (within reason- they aren't going to hire you into the BBJ). I know new hires that have gone into the Falcons and G200, as well as the citation fleet. A lot depends on your interview process and the background you come from. Many new hires are placed in the citations.
I believe that the company has the right to place you into a domicile based on their needs, however they have been asking new hires where they want to be based, and for the time being seem to be sticking to the requests. IIRC, the formal job offer designates both the fleet that you are being hired into and the base you will be domiciled at.
Upgrade varies, and certainly the new contract should change things up a bit. It has been roughly 9-12 months for the citations and about 2 years for larger aircraft. Nobody really knows how things with the new contract and seat locks will pan out until things settle down. Certainly my buds over there expect upgrade time to lengthen a bit.
Hope that helps... from what I hear from friends over there and have seen of their operation, it certainly seems like a decent place to be.
~J