The regular New with the long comb seems to be the easiest to come by, in my experience, and is my favorite. This is a hard razor to beat. I didn't really find much, if any difference between the LC and the SC. 1929-1940
http://wiki.badgerandblade.com/Category:Gillette_NEW_Razors
The new deluxe has a flat back, and is a bit more aggressive. 1930 and 1935
http://wiki.badgerandblade.com/Category:Gillette_NEW_Deluxe_Razors
The new improved actually came out first, but I can't tell you how it shaves, because I don't have one yet. 1921-1929
http://wiki.badgerandblade.com/Gillette_New_Improved
Thanks! I did start finding some threads but that Wiki info is just what I needed.