I personally think Peyton to the Jets is a long shot (just to let you know I see him going to Kansas City or Arizona) but on the chance he does come to us the future stability of the QB position becomes a concern.
In order to get Peyton cutting or trading Sanchez and saving the 9+ mil cap space is almost a given. That would leave the backup space still open, but the type of backup needed would be different. No longer do we need a solid QB 2 that can push a young Mark Sanchez, but one that could come in to replace an injury prone Manning if the neck acts up again, and one that we can develop to be the QB for our future after Manning. Our two options would be A) FA or B) Draft; pretty obvious, but who we target in each is now different. We saw in the past draft the Patriots select what they hope to be their QB of the future in Ryan Mallet who they want to develop and replace Brady the day he inevitably retires. We also saw a similar thing in Green Bay when they drafted Aaron Rodgers to be groomed to replace Brett Favre after he retired.
Free Agency: A Chad Henne, Jason Campbell, Brady Quinn type player no longer is as necessary to push Manning because well I don't think Peyton needs to be pushed, the benefit of signing one of these guys is that they provide a solid backup that you can trust if your injury prone QB goes down, the downside, none of these guys are guys that can improve significantly and provide the solid starter (at least) for years to come after Peyton retires. Signing one of these Free Agents will just continue the revolving door which is the Jets starting QB position.
Brandon Weeden: Weeden is a solid QB prospect that would likely be a first or second round pick if it wasn't for his age, and that is the major concern I have with drafting Weeden. The Brandon Weeden situation is the same as the FA QB situation, I'd feel comfortable with him coming off the bench, but I expect Manning to play at least another 2-3 years, which would mean at that time Weeden would not be 24-25 like most QBs coming out of the draft this year but 30-31 an age past physical prime.
Brock Osweiler: Brock is likely going to go in the 3rd round. He is rated 29th by Scout's INC overall and Kiper has him as the #5 QB in the draft. Osweiler did impress at the East-West Shrine game earlier in the year, and I think this is the best move the Jets could make for their future. Osweiler would not be the best backup we could have, but he wouldn't be the worst. He also provides a good base to develop for our QB of the Future. WIth his projected spot as a 3rd rounder he gives us good value at the pick and lets us keep our first and second rounders to use on more pressing needs.
Ryan Tannehill: Ryan is the third best QB in the draft, but there is a large drop off between #2 and #3. That being said Tannehill could still possibly be a top 10 pick and probably a first rounder. Tannehill would be the best QB for this Back-up/Prospect role. He would cost a first rounder, which might be too much for a backup, but Green Bay did something similar with Aaron Rodgers. Tannehill would follow the same path as Rodgers; a first round pick who would back up and develop while observing how a Hall of Fame QB succeeds in the NFL. The problem with Tanehill is his location in the draft. Tannehill could very well be picked by the team that loses either the Robert Griffin III or Peyton Manning sweepstakes; that would mean the Jets would likely have to trade up to draft their backup. The Jets have so many needs trading up to adress one of the major ones might not be a great idea because of the need of depth on this team, losing that depth for a backup QB doesn't seem like a smart decision. This route likely has the highest upside in the future, but is the least plausible route possible.
Of all of the choices, I believe taking Osweiler in the 3rd is the best, he's doesn't have a grimm future, and it keeps the Jets' first and second round picks available to take a more important need like OLB, or Safety.