On a new brick wall, the parts that matter most are the ones you won't see once it's done. Brick veneer is built on the understanding that some water will get through the brick, so flashing, a waterproof strip set into the wall, and weeps, small drain openings along the bottom, carry that water back outside through the air space behind the brick.
We check the flashing and weeps as the wall goes up rather than at the end, because once brick is laid over them there's no easy way to look. Before the first delivery, we also set aside a dry spot on your property so the brick and mortar mix stay out of rain and melting snow until we use them.
If you'd like natural stone instead of brick, or stone set alongside it, our stone masonry work covers that. And if you already have a brick wall that's sound but has worn joints, brick pointing, which replaces the old mortar, is usually the smaller and better job than building new. I'll tell you plainly which one your property needs.
A freestanding garden wall has a different problem. With no house behind it, a thinner brick wall can only stand so tall and so long against wind and sideways push, so it needs a thicker base, piers or a zigzag line to stay firm. That choice changes how the wall looks and how much of your yard it takes up.