The 37 came from your small chainring's 26 teeth plus your small cog's 11 teeth. The least number of teeth you can use at any one moment is 11 for the rear cog + 26 for the small ring, or 37 teeth. Your chain needs to enough extra links though, to accommodate the 34-tooth cog + 48-tooth ring. The derailleur needs to be able to extend to "soak up" those extra links.

By SGS, I mean long cage. I believe that SGS is an abbreviation for something; I forget what.

As far as choosing between SRAM and Shimano cassettes, I personally do not have much in the way of a preference between the two brands. Both are good.