On the surface, the Bears have 20 FAs with only 20 mil and essentially 2 draft picks (top 125) to add talent. But a closer look shows, there's not really a whole lot the Bears have to lose and most of the FAs are extremely replaceable.
I'd cut Sims today. I'd probably also cut Sowell. 1.5Mil is a lot for a backup OT/goalline TE. Acho is another possibility to cut at 2.2Mil savings. I would also expect Kyle Long to be restructured or take a pay cut.
Bray- wasn't on 53 over 1/2 the year. Doesn't need replaced
Cunningham- 4th RB isn't necessary, was essentially a special teamer only. Can fill his spot with any position and cheaper than 1.05Mil he got this year.
M. Burton- FB was inactive most of the time. Ryan Nall can take his or Cunningham's roster spot with no drop off at league minimum
Kush- didn't play the last 12-13 games. Could be replaced by a similar player for less than 1.35 he got paid
White- obviously gone. Was inactive most of the 2nd half. Wims is the 4th WR next year
Zach Miller- obviously never active, doesn't need replaced on 53
Nick Williams- anybody even know he was on the roster? 6th DL all year, not necessary. Can be replaced by player at any position.
Marcus Williams- Bears had him or Cooper on the roster all year. Neither played much. 6th CB, league minimum type
RRH, Scales, DHC, Braunecker, Coward, and Irving made a combined 3.2Mil last year, and I'm not even sure all of them counted toward the cap due to the top 51 rule. All are RFA or ERFAs. Should bring them all back for a similar cost, and the last 4 don't even have to be guaranteed a roster spot.
I'd probably bring back Witzmann and Bellamy for depth. Long will probably get hurt again. Witzmann was OK in his spot. Could probably be re-signed for 6 digits again (790K this year). Bellamy would probably take a deal similar to the 2 year/3.5Mil the Bears gave McManis last offseason.
That leaves Callahan, Massie, Amos, and Lynch.
I don't think there's any way you re-sign Lynch or Amos. Lynch got 6Mil this year, and i don't see him taking a paycut to come back, even with long-term security, unless he just really worships Fangio. Acho is still under contract so he could be the vet 3rd pass rusher (could also be cut to save 2.2Mil). But Lynch was signed before the Mack trade and I'd imagine he wouldn't have been if the Bears already had Mack. They do now, he's expendable.
Amos is probably going to get a big contract, he's the top FA safety other than Landon Collins, who is likely getting franchised. Amos is a really good player, but more power to the team that signs him to a big deal. Probably the least important position on the Bears D as constructed, and Bush is probably the most proven capable backup on the back 8 of the defensive side of the ball. No-brainer to let someone else give him a multi-year deal and reap the rewards of a potential comp pick in 2020.
Massie I'd look to bring back. If he'll take similar to the 6Mil he made this year on a 3-year deal (with a year or so guaranteed), he's worth the money as a potential upgrade would cost much more money. Anyone cheaper would be a downgrade in ability. Could gamble on a starting caliber OT being there at 87 or Coward taking a huge step forward, but those seem like really easy ways to get your QB messed up and ruin your season.
Callahan i'd probably bring back too, but Massie is more important IMO. Again, I think we're looking at about 6Mil/year. Be tough to offer him long-term with his injury history, but probably have to do it. IF not Callahan, there's some decent slot CB talent available. Darqueze Dennard, Kayvon Webster, Justin Coleman, Steve Nelson Jason Verrett are all guys who could be similar cost to Callahan and are of similar ability. But familiarity played a big part in bringing back Prince and Fuller, so I'd imagine the same would hold true for Callahan.
That would bring back all 11 starters, along with Cohen, the top 2 reserve WRs and the top reserve OL (Witzmann). On defense, you only replace Amos with Bush and bring back all other contributors save for Lynch.
As for the draft, with the first 2 picks....you don't need an immediate starter which is good because you aren't getting immediate starter talent. So, I'd look most closely at finding potential long-term solutions for players who are older and/or near the end of their contracts. So, looking at long-term replacements at RT, RG, CB (for 30-yo Amukamara), SS (Bush a FA after 2019), RB (Howard FA after 2019), OLB (need a rotational guy, plus Floyd's 5th year option is 14Mil+ in 2020).