Look for a reasonably straight stick that is at least 1″ (2.5cm) in diameter. It should be slightly larger around than is comfortable to hold, so you can carve off some of the wood and still have a stick substantial enough to support you while you’re walking. You want a branch with enough wood at the top to provide carving stock, but that has a slender enough shaft that it won’t be hard to reduce it to a suitable diameter.
Almost any kind of wood will work. As you carve more, you’ll learn what you like to carve. You’ll also become familiar with the varieties that grow in your neck of the woods. To help you get started, though, here is a chart of the trees I have carved and my notes about their suitability as both carving projects and hiking walking stick.