If you're looking for a good safe hardwood I recommend oak.
I've been collecting branches for my snakes myself and I look for oak and maple trees. If you're not sure what they look like use Google to try to ID by bark. It's harder in the winter when all the trees don't have leaves. Oak and maple have distinctive leaf shapes when in leaf.
Also if you can try to find branches that are freshly fallen. I use a handsaw to cut branches about the size I need, and trim them up further at home. Hand saws are only $10-20 at Home Depot.
Anything that's been rotting on the ground for awhile will have mold and fungus, not be as sturdy and stable, may deteriorate over time and you may not be able to sanitize rotting wood properly. Avoid anything that's been on the ground for awhile.
I bake my branches in a 250degree oven for at least an hour. After stripping off any lichen or moss. I leave the bark on my mine personally. Haven't had an issue with anything catching fire.