Coaching-staff junkies (geeks) like me get into the minutae a little harder than most, by design. So the first new staff since 2002 comes with new questions. Here, I'll try to answer (guessing, in most), questions I'd be most concerned with.
Will the coordinators be in the booth or on the field?
Rob Chudzinski will coordinate the offense, and may prefer the coaches' booth. He sat in the booth for San Diego the last two years, though Norv Turner did most of the playcalling (offensive coordinator Clarence Shelmon, who handled the running game and OL protections, was up there as well). I can't find info on Chudzinski's Cleveland tenure or Miami coordinating.
As would be expected, Mike Shula would call the plays to the QB.
On defense, Sean McDermott has called exclusively from the sidelines. He tried it once from the booth, and it didn't work out. Ron Rivera called from the sidelines as well, in San Diego, but did from the booth with Chicago. The only thing that would push McDermott to the sky would be an insistence from Rivera, based on how much/little input he'd want of his DC on the sidelines. Chances are, given the choice, McDermott would put former DC Ron Meeks in the booth, which is what would make an assistant DB coach (preferably a young one) a critical hire.
I prefer coordinators on the field, personally. Most teams put the WRs coach up there, and possibly the OC if wanted; they generally put the DBs coach up there, but some coordinators work from there on defense as well.
Chudzinski is a disciple of the Don Coryell offense, getting it directly - Coryell taught Ernie Zampese, who passed it to Norv Turner. Coryell's offense has additional roots in Sid Gillman from the 60s.
It's a very vertical offense, though Turner's variant is considered more QB-friendly and takes more controlled chances. Mike Martz pilots the other, more open and aggressive form, though that seems to have calmed down more recently in Chicago. It has a lot of timing routes and precision in routes, and relies on a power running game from zone blocking (the last of which shouldn't be much of a departure).
It's expected to be an odd-front 4-3 again, as they have been under John Fox (most 4-3 teams, honestly, do this anymore). Under tackle and nose-tackle combo inside, ends outside the OT. Only difference seems to be using the SLB on the line more.
But don't expect the same passive cover 2, or the disguise-scheme cover 3 base. Jim Johnson used extensive blitz packages and fire zone/zone blitz packages, and there's no reason to expect less of Rivera/McDermott.
Coverage base? Whereas Fox used a lot of disguised cover 3, and then Meeks' Tampa 2 using 2-deep and single high safety looks, the Jim Johnson defense varies things up much more. Expect more varied coverages and man coverage.
As for nickel, expect more 3-3 scheme and less vanilla 4-2 front. At one point, McDermott ran a 4-0-7 dime, putting a safety in the box in lieu of a single linebacker in the dime (he didn't have a Beason/Davis situation, however).