I'm going to play the role of the front office and layout a short list of very plausible goals in order of importance. These won't cover every need of course, but these are the minimum necessary to win the offseason.
Double up on the QB position
Clearly this is the most important position in football. Reports are telling us that Mike Glennon is coming to the Bears come hell or high water. He is 28 years old and has some decent film as an NFL starter. It's unclear as to whether or not he will find success as the Bears' signal caller, but his turn is next. The goal here is to not stop at Glennon. A high draft pick at the position gives us more opportunities for a stud. Even at pick #3, you're looking at a franchise guy should Glennon cap out at a bridge player. In the worst case scenario, both fail to pan out, but your odds are better than a 50/50 shot with one guy. Besides, if somehow Glennon lights it up and the young QB becomes unnecessary, these guys are selling like hot cakes. You could trade your young benched player to a needy team and maybe get equal or an even higher value return than you invested.
Sign one corner and draft another
We just need a lot more talent at this position. I think Stephon Gilmore is our guy to lose, but even if we do, there are a number of other strong names in free agency at the position. We also have to draft one because, this is the deepest CB draft anyone can remember. In the first 3 maybe 4 rounds the best player available (and maybe even the next one) is likely to be a corner when you're on the board. Additionally, Kyle Fuller has one year left on his contract and is really going to need to have a stellar year. This gives us options in the future.
Draft a TE
Like CBs, but not quite as proliferant, there is a wealth of tight end talent in this draft class. Zach Miller is 32 and even so, the team could do with 2 TEs worthy of sharing the field on a good number of snaps over the course of the season. So draft musts become QB, CB, & TE and I think the team should consider trading up if they miss out on either of the 3 before the 4th round (trading back at #3 for more picks is possible too but always a pipe dream for us on the outside looking in). Less experienced QBs, as we will have, will appreciate the big-bodied outlet that TEs provide.
Sign a veteran WR
Many would like to see Alshon Jeffery return to the Bears. Even more agree with that if the salary he commands is reasonable. That would be ideal, but barring that outcome, a veteran with a strong track record needs to be involved in the offense and mentoring the group. Dependability and consistency are the quintessential needs. Kenny Britt or Kendall Wright may be suitable, but even a reasonable trade scenario could net an experienced leader.
Cut ties where we can
Jay Cutler, Lamarr Houston, & Eddie Royal are going to open up a lot of cap space. They have an injury history and are not young talent to develop. All 3 are going to be really difficult to move on the trade market. If negotiations are dried up, just give them their walking papers. Rebuilding a real Super Bowl contender is going to take years and that money needs to be available in the future to extend performers and buy upgrades.