Most new GMs coming from other teams would focus on keeping Jake Long, Randy Starks and Sean Smith.
Jake Long and Randy Starks would be re-signed because they're two of the very few players the Dolphins have on roster that are universally respected around the league. Whatever new GM comes here is going to be very defensive. He's coming into a new situation (probably a first time GM), doesn't know how much winning talent he'll have at his disposal, and so he's going to want to keep the few guys he already knows to be really good. You can worry about resource allocation some time down the road when you've engaged your own talent acquisition program long enough to actually be bumping up into your resource constraints (i.e. salary cap). The Dolphins aren't close to there yet. The concept of this roster having trouble staying under the salary cap is laughable.
Sean Smith would be kept simply because of the universal league-wide emphasis on keeping and acquiring talented corners. The passing game is too important to NFL success. Smith is not universally respected by any means but the Dolphins' lack of corner talent coupled with the league emphasis on corners would outweigh the chance that whatever new GM comes in wasn't particularly a fan of Smith's when he came out of the Draft.
Guys like Reggie Bush, Brian Hartline and Anthony Fasano...flip a coin. Some prospective GMs would be fans of theirs and many would not.
Dan Carpenter, Richard Marshall, Richie Incognito and Kevin Burnett would be prime candidates to be cut so that the new GM could try and bring in some of "his" guys. And it goes without saying that a Tony McDaniel would be allowed to walk on his expiring contract.
Matt Moore would be a coin flip. Up to him whether he wants to go ahead and still try and be a starter somewhere else (unlikely to have very many opportunities laid out before him) or if he'll accept a backup's contract to continue being the backup in Miami.