Now you are in the right ballpark. I wouldn't expect the best selection of tube at a sheet metal shop. 1/8" wall is pretty stout for that, but you will find it a lot easier to weld than the 16ga.
Depending on shipping there is always onlinemetals.com You are not that far away from a depot so the shipping might not be too bad. You won't have to worry about transport, but you will be limited to 8' pieces. At least it's a great place to look up common sizes and get some ballpark pricing. My local steel yard is usually 20-50% lower depending on the material.

Not sure how far you are away from THIS PLACE.

BTW When calculating for miters, you might want to measure square tubing on the centerline. Because the corners are rounded, it doesn't lend itself to making accurate layout lines form the max or min length sides.