The Plumber’s neck (Newport) is a medium offset, quarter toe hang, and works well for a gated slope.
The Flare neck (2.5) has a bit less offset and gives the putter a bit more toe flow. These work well for players that rotate the head open and then shut through the stroke.
No Neck (Squareback 1) These are pretty much face balanced and are there for players who like a clean look at address. These work best for players that putt SBST
Longneck- These look like a plumber’s neck only longer. The length changes the balance of the stick, and generally makes putters more face balanced than a regular plumbers neck. These also work well for SBST
Slant Neck- This looks like a plumber’s neck without the elbow. The bit of offset gives players a less obstructed view of the ball. This neck usually has a quarter toe hang and works well with a gated storke.
Center Shaft- I’m not sure if Scotty makes one that’s OTR. This design typically is associated with a flatter lie angle. Also, the center-shaft position places the swing axis closer to the golf ball. I’ve honestly never putted with a Center Shaft.
Once you determine which is your dominant eye you basically choose a putter that looks best to you. The eye dominace along with offset selection is to aid in alignment. Once you determine that you need to figure out whether your have a gate stroke or a straight back straight through stroke. That will narrow your selection even more.
It does take some time and some trial and error. Our biggest piece of advice would be to get fit by a professional prior to making any big decisions.