As a huge Reid fan from Philly who has followed him closely for 14 years and who "gets" him (unlike most in Philly), let me offer some thoughts on how I can picture Reid handling the QB situation.
The first thing we need to remember about him is that he tends to be full of surprises, which means that even thought I "get" him, I'm probably wrong about all this.
Secondly, he strongly favors QBs who make good reads and intelligently and quickly go through their progressions. This would be bad news for Geno Smith, as it is his one glaring weakness. However, it was also bad news for Michael Vick, as it was also his. The flip side to all this is that as much as Reid values this trait in a QB, he also believes he can coach a QB in this area, so in a way it's a contradiction. It's what he most looks for, but since it's what he can coach and since he can't coach athleticism, it might also be something he least looks for. All that having been said, my best "guess" is that he does not have a #1 overall grade on Geno Smith. Probably likes him. Thinks he can coach him up. But that he's not a finished product and he won't want to struggle with him the way he struggled with Vick, at least not at the cost of #1 overall.
The way the Eagles were run when they were most successful was to stick to their "board" as far as value is concerned. They always got into trouble when they "reached" for a player based on need at a position. Reid referenced this in his initial press conference. If they don't have a #1 overall grade on Geno Smith, I really don't expect them to draft Geno Smith #1 overall, no matter how badly they need a QB. But that doesn't mean that Reid won't have a plan to deal with the situation. He will, and it will be a good one.
Veteran QB: More than likely, prior to the draft, a QB will be brought in to be the "starter", will be capable of starting and playing well in an Andy Reid system, will be a major upgrade over what is in KC now, will give them the leverage to not HAVE TO draft a QB #1 overall, and then no matter who they take in the draft, the veteran most likely will start the season as the #1 QB. Doug Pederson (yes, THAT Doug Pederson) was brought in for that role when McNabb was a rookie.
Ties to other QBs: Reid directly or indirectly has ties to several QBs who come to mind: Kevin Kolb, Nick Foles, Matt Hasselbeck, Matt Flynn. No, Michael Vick is not coming to KC. Yes, Reid loves him as a person for having turned his life around, but he simply can't play anymore and Reid knows that. He's a 32 y/o running QB. Reid coached Hasselbeck in GB and Flynn was a QB in GB in the same system, even though Reid didn't coach him, so I'm including him.
Kevin Kolb: Could be available in a trade for a mid round pick because of his roster bonus. Don't underestimate how well Kevin Kolb could play in an Andy Reid system. Kolb was the first QB in NFL history to begin his career with two straight 300 yard passing games (that's right, out of everyone in NFL history) and in fact, I believe one of those games might have been against the Chiefs. He lost his starting job to Michael Vick only because of injury and because Vick was simply the best QB in the entire NFL at that time (it was a short time, but he was). Vick had the highest QB rating in the league, which didn't include what he was doing with his legs, and finished 2nd to Tom Brady in MVP voting, and Kolb only lost his job to him because of injury. Kolb was pretty good. Keep in mind that the Cardinals stink, so it's tough to judge him there. But keep in mind that they went 3-1 with Kolb, who had an 86.1 QB rating, and 1-11 with Skelton, who had a 55.4 rating. (Cassel had a 66.7 rating for comparison).
Nick Foles: Depending on what the yet to be determined new coach of the Eagles thinks, they may or may not want to keep Foles, but make no mistake, this guy can play in an Andy Reid system. 9 out of 11 starters on offense were out with injuries when Foles took over, including 4 out of 5 offensive linemen, DeSean Jackson - who stretches the field and opens things up for everyone - and LeSean McCoy, who takes all the pressure off of the QB. Foles had no time to throw and no one to throw to and still played quite well for a rookie. Has all the tools. He can play.
Bottom line: I could picture one of these guys coming in (Kolb, Foles, Hasselbeck, Flynn). Reid saying, "He's my starter. He can win a championship for us," and he wouldn't be lying. I could then see him identifying a QB that fits what he wants to do, projecting where he should get draftd, and trading down to address several needs and getting his guy anyway. Then if the team loses a few games, the rookie starts at some point during the season.
Just my $0.02