Moved from the 2019 season discussion:
Well, you're working with two different definitions here.
Who might I want to keep? Excluding players with long-term contracts (and even they can be traded - Harper has a FNTC, but nobody else does). As you noted, maybe Eflin. Haseley.
Hoskins. Some of the young pitchers.
But in your second paragraph, you changed the terms. Who would I want to sign to a long-term deal at this point? Well, nobody on the pitching staff. For the arbitration-eligibles, I would recommend just going year to year - either because we just don't know about them yet (Eflin, Velasquez), or because they're relievers, and prone to collapse.
Non-pitchers? Realmuto. That's a no-brainer. Nobody else; the only younger players I really care about retaining, to see better what we have (Hoskins, Haseley, Quinn) aren't even arbitration-eligible. Tender them contracts with modest increases - I see no reason for any Kingery-type prospective long-term deals (given Hoskins' second-half struggles).
Nor do I recommend prospectively signing Alec Bohm or Bryson Stott to "Kingery deals" at this point in time. I mean, Bohm in particular might very well to go spring training next March, and explode the way Kingery did in 2018. If that happens (and assuming the same people are running the front office as were two years ago), I wouldn't be surprised if they treated Bohm the same way they treated Kingery - sign him for several years at what are likely to be favorable salaries, and bring him north to play 3B... but that doesn't mean I'm anticipating that, or recommending it. All things being equal, I'd like to see Bohm get some time in AAA.
Beyond that... potential non-tenders among the arbitration-eligibles: Morin, Parker, Knapp, Franco, Gosselin, EIckhoff, Morgan.
Options to buy out: Vargas, Hughes, Neshek.
Free agents to pat on the fanny and thank: Smyly, Nicasio, Morrison, Rodriguez, Hunter, Dickerson.
Free agents to talk to about coming back: Nick Vincent, Brad Miller. (Dickerson will be too expensive.)