If I'm Andy Reid taking over the Chiefs... he could easily totally turn around their offense this offseason. They've got plenty of cap space so I'd resign Dwayne Bowe and Branden Albert both. Take Geno Smith with your 1st pick (hopefully you can move down a bit and get him without using the 1st overall pick), draft Stedman Bailey to keep playing with Geno...
Andy Reid could do a lot with Geno Smith, Jamaal Charles, Dwayne Bowe, Stedman Bailey, and Tony Moeaki. All of those guys are REALLY good fits for his offense and with his track record of getting the most out of quarterbacks... they could pull a real turnaround next year.
Scott Pioli is out in KC ....
KC should fall into place very quickly.
Reid as HC, Mornhinwheg or Shurmur as OC, Castillo as OL coach, probably Brad Childress as QB coach. If Lovie doesn't get a HC gig he could easily step in as DC, if Ron Rivera gets booted from Carolina he's also a DC candidate. If Reid has his way there's your coaching staff, albeit an expensive one.
Say what you will about those guys but all of them are proven assistants. With that coaching staff and a good draft class that includes at least a decent rookie QB, Kansas City could easily challenge Denver for the division next year, or a wild card spot at a minimum.
They're a couple players away from serious playoff contention. If Geno Smith pans out at all, they re-sign Branden Albert, and add a little help in the draft at WR, CB, and DL, they will be fine. Their problem has been that since 2010 they haven't even gotten mediocre play out of their QBs, all they need is a signal caller who doesn't make a ton of mistakes and gets the ball to his playmakers.
I wouldn't be surprised to see them make a run at Greg Jennings or maybe Mike Wallace. I also don't know if they'll target Geno Smith or not.
If I were Andy Reid, I'd sign Mike Vick (since he already knows the offense) and try to trade down. If I HAD to pick #1 overall...I'd probably go for Star Lotulelei or Luke Joeckel. I would also try and retain Brandon Albert and kick him inside to guard, draft Joeckel, and then in the 2nd/3rd rounds look at guys like Aaron Murray or Tajh Boyd. Then look at receivers like Ryan Swope, etc.
Andy Reid made the Eagles a consistent playoff contender despite never having an elite QB or elite WRs. McNabb and Vick both put up great numbers in his system despite not being elite talents. AJ Feeley and Kevin Kolb looked pretty good in his system but turned out to be complete duds outside of it. All the Chiefs will need with Reid's system is competent QB play, he has Jamaal Charles to play the Brian Westbrook role. If the Chiefs can secure a decent QB and #1 WR in FA like Bowe or Jennings Reid will immediately have more skill position talent than he ever had in Philly. Even if they don't do that they can make do with Steve Breaston (who the current coaching staff hates for some reason but he's not a bad #2 receiver at all), Dexter McCluster in the slot, and a talented draftee that fits the WCO like Da'Rick Rogers, Stedman Bailey, Ryan Swope, etc.
In terms of getting said QB IMO the ideal option is to find a way to get Geno Smith without taking him #1 overall, i.e. trade down with somebody who really covets Lotulelei, Joeckel, Jarvis Jones, etc. hopefully to around the 10 spot or so, that should get you a 2nd rounder. Use that 2nd rounder on a DL prospect like Shariff Floyd, Kawann Short, etc. to replace Dorsey and/or Jackson (both of whom are extremely overrated and easily replaceable IMO). Don't forget they also have Dontari Poe on the roster and he can play NT and DE.
I think Geno Smith is the best fit for Reid's WCO by a pretty big margin, but he's not a top-5 overall type of QB prospect. If they don't go with Smith then like you said I'd maybe take Aaron Murray, Tajh Boyd, or Tyler Wilson.
EDIT: I just realized this and I thought I'd throw it in cuz it's funny. I totally forgot the Chiefs even had Jonathan Baldwin on their roster. Kind of crazy because I really wanted the Ravens to draft him in 2011 and I liked him a lot as a prospect. He has been a huge disappointment as a 1st round receiver and who knows what his future holds? But again maybe Andy Reid can get something out of him...
If I had a guy like Baldwin who was struggling some, I'd just start throwing him 3 or 4 guaranteed completions a game. Screens, drags, short hitches, etc... get the ball in his hands and see if he can make a play. If he can't make a play, be patient. After he's made a few catches and gotten a few tastes of the defense, then you start trying to work him in on the harder stuff downfield.
Hey, wait... that sounds familiar. Don't we have a deep threat WR who struggles with the mental aspects of the game at times? The Ravens could really stand to learn this lesson with Torrey Smith, and under Caldwell they might be getting there. You can't just expect him to catch 3 deep balls a game and nothing else. Hit him with a screen or a slant a couple times to get him going and THEN try the deep stuff.