Gary Suter.
Niedermayer only chose Anaheim because of brother. Stamkos met with Sharks brass/owner.
There was another big name who was interested in coming but Sharks didn't have ability ($$ permission) to sign more than a decade ago. (I'm not remembering the rumored name)
Depends on age (how close to retirement) and whether winning cup is a top priority in the near future. And/or player wants a challenge to change "fortune" (assumed winnability) of team.
We had also traded for his rights the week before free agency began (back when that was a thing). He publicly stated that the showing of commitment was a deciding factor in signing with the team.