At a recent class, there was a newbie who sat next to me. She had bought/brought a 12x18" mat and a 6" ruler which were not quite big enough. I would suggest a mat at least 24" long so, when cutting a strip (where fabric is usually 42" wide) from selvage to selvage, you can fold it in half and, now measuring 21", it will fit on the mat. This is also why a 6x24" ruler is best, in my opinion.
As for scissors, I keep a small pair at my machine to snip threads and a pair of Fiskars on my cutting table. Just make sure no one uses your scissors for something other than fabric; it does make a difference. Using a Sharpie, or some other permanent marker, I label mine on the blade.. "Fabric only" ... "Paper." Glad I did. The last time I tried to use the paper scissors on fabric, it was a struggle!
One last note... label your mat, ruler, and scissors with your name before going to class. With so many of us buying the same tools, things can get mixed up very easily.
Have fun & welcome to our world!