SG's are great for sure, been playing them since the late 70's. I prefer thick necks and the 2011 I have now is super thick. The cool thing about them is that they are available in almost any configuration you can think of.
Skinny necks, thin, fat...mostly 22 frets but some 24, P-90's, humbuckers, mini humbuckers, single coil.... ebony necks, rosewood necks, baked maple...body wood mostly Mahogany but there is Korina and flame maple out there too....stop tail, Gibson vibrato...even Steinberger tail pieces.
Can be custom shop or regular production, all kind of levels of trim from Supreme style, Custom, Gibson Standard, just about anything you can think of has been made one time or another
Lots to check out and play, just depends on what you like. Enjoy the hunt, killer guitars.