First on the offensive side of the ball. Look for Ryan Mallett to be a name thrown around at quarterback. The former Patriots backup was with the Texans (Mike Maccagnan connection) this season after a trade, and is scheduled to be a free agent. His potential is still unknown, and he would be good competition for Geno. Watch for CJ Spiller's name to be thrown around if he is cut and Gailey becomes the offensive coordinator. Spiller was most productive in his early years in Buffalo when Gailey was the head coach.
On the defensive side of things, two big names I expect to be thrown around are Sam Acho and Brooks Reed. Acho played for Bowles, and Reed was drafted by Maccagnan. Both would be good fits in the Jets 3-4 defense, hopefully replacing Calvin Pace. In the secondary I expect names like Kareem Jackson, Antonio Cromartie, and Kendrick Lewis to be floated. Obviously Jets fans know Cromartie, but Kareem Jackson is the guy to get at cornerback. He is young and athletic, and can be a great fit in the defense the Jets want to run next season.
Both Maccagnan and Bowles seemed to have close relationships with players from their previous spots. This makes me think the Jets will attack some of their guys in free agency. This is something to look for come March.