At your height and weight I would tone the size down a notch. Get a board thats maybe 156-158 since you are used to bigger boards. I'm over 6' and a little heavier and I have ridden 151s. The reason why you were started on a 161 is that smaller boards are a lot less stable at high speeds but super maneuverable (carving, jumps, jibs etc.).
A 156-158 will be almost just as stable as a 161 with a little added maneuverability, perfect for you to start stepping up your riding.
Definitely go to a core shop to find the boot that works best for you. Get it fitted to you down to like OJ's glove. Then go online and start hunting for deals on that *exact* model and size.
Buying all Burton is definitely the most seemless way to go. Again though, boot fit is incredibly vital, so if Burton boots just aren't for you don't be afraid to move on.