Critical need: QB (plus GM and HC, duh). Nothing else compares, and I believe (and always have) that a real QB would do a lot for other positions, too.
Major need: ILB (needed a starter next to Derrick Johnson for a couple years now) and CB (one of many epic Pioli fails resulted in one of the best CBs in the league leaving in FA, so the talent is thin and depth non-existent behind Flowers).
Need: WR if Bowe leaves (would be stupid of a new GM, and a new QB and fat contract should entice Bowe, but the bridge might be burned). More DL - as usual. Dorsey and Jackson could have roles on a team, but they're both ridiculously overpaid. Safety - Berry hasn't been himself this year after a lost 2nd year, so the jury's out, and he has no partner to speak of.
Depth need: RB; another WR perhaps; interior OL but not in the first 3 rounds; another QB; more DL; another LB; definitely CB and probably safety too.
Developmental need: another QB
On paper the Chiefs are better than a team like Indy, but they desperately, desperately need production at the QB position. If they find a guy who can give them that, the entire team will be better off. Once you find that QB, then you can worry about filling out your roster, in KC's case particularly the defense, which Pioli has inexplicably fudged since he got here, with the lone exception of stealing Justin Houston in the 3rd, but that's more than offset by his other blunders.