This should help with your putter question. http://www.mygolfspy.com/how-to-choose-right-putter-hosel-shape/   

I'm pretty sure necks affect the balance of the putter and help compliment different stroke styles.  I'm sure there's more to it, but here's a the little bit I know:

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.

As for welded neck I think that’s a FTUO feature.

I'm by no means an expert at all the different necks but I have owned several SC putters in my time.  IMO there are a few different neck styles that make up his collection.  Theres the plumbers, 1.5, 2.5, flow neck, straight shaft, long nect, mid slant, etc...this could go on and on. 

From what I know and from reading on www.scottycameron.com there are different suggested necks for eye dominace.  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.  My biggest piece of advice would be to get fit by a professional for a putter.  They can get you set up and make sure you have the correct length, loft, lie etc.....check out www.mygolfperformance.com for some a guide to a 5 minute putter fitting.

good luck