I look at this as tiers. My tier 1 is young'ish players who could be part of a core. Collins for sure is in this group, maybe Ball, and possibly even Markkanen. Any of these would require a significant sign and trade, probably involving both Smart and Thompson (we would need to clear salary as we would be hard capped). I don't see any of these as likely. If we can get Markkanen in a S&T for say Thompson and Langford or something like that, that is pretty good. I am not really in for Ball but I would be happy with Collins or Markkanen but see any of these as very unlikely.
Next tier is the players that may not be stars (or stars anymore) but we could get with the Taxpayer MLE (about $6M I think). I say taxpayer as if we use the non-taxpayer (more like $9M), we end up hard capped. I see players like Bobby Portis, Lowry (maybe a stretch), Rose all in this range possibly. If we could get Markkanen in this range, great but I doubt a young big like him goes for that. It would be a big raise for Portis over what is got with his last contract. He would be potentially a really good fit but he would have to play as a PF.
The next tier are all the older, in my opinion too old names that get thrown out. Gay, Green, Milsap, Markieff Morris, Rose. I am really not all that interested in any of these guys. Let them go to the Lakers, Nets, Buck, whatever.
The final tier are players like Olynyk and Mills. These guys will probably still get some decent money but are not even starters on the Celtics. I don't have much interest in these players either.
Rich Signing (up to $20M): Collins for Smart, Thompson, and probably more
Ball for Smart, Thompson
Medium Signing (+/- $14M): Markkanen for Thompson and Langford
Lowry for Thompson and Langford
MLE (Non-Tax, $6M): Bobby Portis