Here's how I'd play this out if I were the cubs. Right now if you use MLBtraderumor's arb estimates the cubs have $136.3M on the books for 2018. I'd keep La Stella at $1 mil. I'd likely try to re-sign long term Hendricks, Bryant and Russell but obviously you keep them at $4.9 mil, $8.9 mil and $2.3 mil. I'd non-tender Grimm at $2.4 mil, Rondon at $6.3 mil and Martin at $4.9 mil. I suppose you gotta consider keeping Wilson at $4.3 mil especially given he and Monty are your pen lefties. So with those 3 nontenders you're looking at $13.6 mil comming off the $136.3 mil for a total of $122.7 mil.
I'm going to play with a couple assumptions. 1) cubs want to be under $197 mil luxury tax. 2) the cubs keep ~$20 mil under that for in season moves. That leaves you $54.3 mil to play around with. Needs would be back up C and a 5th OF positionally if you go with 12 bats and 13 pitchers. Other 10 bats would be Heyward, Almora, Happ, Schwarber, Zobrist, Rizzo, Baez, Russell, Bryant and Contreras. You'd actually also have La Stella, Zagunis, Taylor Davis(C), Ali Solis(C), Chris Dominguez(3b/1b/corner OF), and Caratini(C) Hannemann(CF) on the 40 man as well. In terms of pitching needs you are talking about 2 starters with the other 3 being Q, Hendricks and Lester. In relievers you're looking at Edwards, Maples, Monty, Wilson, Strop needing 3 guys to fill out your 8. Other pitchers on the 40 man are Tseng, Mills, Williams Perez(SP), Scott Carroll(RP), Zastryzny(both), Carasiti(RP), Mills(SP), Butler(SP), Ryan Williams(60 day DL I believe so not tech on 40 man) Luke Farrell(SP I think).
In terms of C Solis is org depth and likely Davis is too. Wouldn't shock me if they non-tender Solis to protect some other guys from rule 5. I imagine if you don't package Caratini that he and davis are your #3/4 C on depth in AAA. For the back up C, I mentioned earlier I'd try to re-sign Rivera to a $2-3 mil deal. He gives you experience and he's decent defensively. If not him I'd look for a similar profile LH C bat at around the same price. In terms of your 5th OF it's almost certainly going to be in house and likely between Hannemann and Zagunis. I'm partial to Hannemann just because he's the stronger defender. Zagunis is purely a corner guy. In my eyes I'd consider him another potential interesting 2nd tier trade piece
In terms of pitching, I'd likely give Carasiti every chance to replace Grimm as your long-ish RH reliever. He's cheap and has good stuff. I think you have to look to re-sign Davis. the pen looks pretty sparse if you're moving Edwards purely to closer. 4 years $72 mil is likely in the range you're talking. That leaves you one slot to play around with. Assuming $18 mil/year on Davis and $2 mil on rivera you're down to ~$34 mil left to play with. More on that last reliever after discussing starters.
With $34 mil left to play with you have options. Let's start with the easier #5 slot. There's a number of directions you could go but I think what the cubs are going to do is sign a vet to a "prove it" 1 year deal with maybe an option and let that player duke it out with Tseng and other guys on the 40 man. Perhaps you even throw in Monty but for my money I want him in the pen. Hard to say exactly who that player will be but to throw some names out that look like potential cubs types... Jhoulys Chacin, Jaime Garcia, Wade Miley(if you think you can fix him) and Andrew Cashner. Think something in the $7-8 mil range gets you one of those guys though you might need 2 years which isn't a huge deal.
That then leaves you with worst case $26 mil. Here's where this gets interesting in my eyes. You're missing one reliever(likely a 7th or 8th inning guy) and a starter. The obvious thing I've not touched at all here is trades. I still believe the cubs are going to move one of Happ or Baez. With Zobrist and La Stella they are pretty covered at 2B to have 2 other guys doing the same thing. Most of the chatter is on trading for Archer or whomever but you could in theory get Davis back and then go after someone like Colome instead. It's estimated he would cost $5.5 mil in arb. $20 mil might be enough to nab Darvish/Arrieta/Tanaka and if you're confident you wont need much in season moves you still have ~$20 mil to play with. Going into the season with $15 mil instead of $20 mil if it's the difference between Darvish and not Darivsh likely isn't a huge issue. On the other hand if the right starter present himself trade wise you could move Happ/Baez plus other parts and use that money on Holland/Reed/Marrow...etc.
So long story short, the only real linch pin from my perspective is getting Davis re-sign. He's realistically the hardest thing for them to replace as they likely need at least 2 quality bullpen guys and other than him there's not a great deal of choice there. With starters you have options in FA even if you have to go down to someone like Cobb. In an ideal world I'd love the cubs and rays to find some way to work a deal for Archer/Colome for say Baez(or happ)/Caratini/Zagunis/Alzolay and one or two others. Rays get salary relief and the cubs fill their two biggest needs.