can I run single wall 6 in black pipe staight from the stove to the adapter coming out of the ceiling? Or do I have to purchase a double wall?

There are two things you need to check prior to using single wall stove pipe. First, make sure it is permitted by your stove manufacturer and local building code. Then check to be sure you have proper clearances. Single Wall Stovepipe requires a minimum of 18" air space clearance, all the way around it. If you have plenty of room and it's permitted, then yes you can use it from stove to chimney adapter. Please note that double wall stovepipe has an inner liner of stainless steel, which gives significantly longer product life. Double wall pipe also means that your clearances are reduced. The DSP for instance only requires 6" of clearance.