I don't think Hamilton is even on Yzerman"s radar. He's the highest profile D available, which means he'll get the biggest contract. A 6+ year term at 8+ mil per is not out of the question. This is not the type of deal a rebuilding team should make with a 28 year old defenseman. Dougie probably returns to Carolina anyway. Pass.
Staal was only here as a salary dump. I don't think Yzerman brings him back as a free agent when better options are available.
Assuming we'll have Hronek, Seider, and Stecher doen the right side, I expect SY will go after left handed dmen that compliment those 3.
DeKeyser and Cholowski will most likely be on the roster. I would pair Cholowski with the more defensively reliable Stecher on the 3rd pairing. DeKeyser could be a fit with Seider (assuming its not top pair duty), but I would rather put him farther down the lineup, perhaps as a 7th D or partnering him with Stecher when it's time to sit Cholowski.
As far as free agents, Stevie should be looking at under 30, left handed D, who could be signed to 2-4 year contracts.
As a defensive partner with Hronek, I would take a serious look at Adam Larsson or Ryan Murray. Neither will come cheap, but I don't think either will need to be signed long term. Considering they'll be playing top pair to start the season, I don't think it would be a bad idea to bring on at least one high end LD.
Seider being more physical and defensively adept, I would look for some help by bringing in a defensive partner with some offense. My choices here would be Alec Martinez or Mike Reilly.
Obviously, Martinez is long in the tooth, but he is a solid 2way dman coming off of a career offensive season. Might be worth a 1 or 2 year deal as partner for Seider until a prospect moves up to replace him
Mike Reilly is a late bloomer. But he's also cheap. He's played well with rookies in the past and has proven himself a solid puck mover over the last season. Could be a relatively cheap signing if Yzerman goes big with Larsson or Murray.
Larsson/Murray - Hronek
Martinez/Reilly - Seider
Cholowski/DeKeyser - Stecher