Best way to attach trellis to brick
I would use something like a long pan-head Tapcon (maybe a 2.25") with a stainless steel spacer. The Tapcon can grip the masonry, and 1" stainless steel spacers are fairly ubiquitous at your local big box hardware store.

Assuming you don't have a hammer drill, buy a normal drill masonry bit. These tend to work better going into brick rather than the masonry, but I would experiment and see which goes in better. If the Tapcon has trouble gripping the hole, break a toothpick in half and stick it in before putting the screw in.