Barefoot is best! Having their toes out so they can maneuver and do counter shifting is very important. Outside, definitely soft soled shoes. We love Robeez mocassins for the very first pair and once they get to actually walking without support more comfortably, we love See Kai Run!
For around the house Bombas socks are the best non slip socks. They actually have non slip gripping all along the bottom not just in a spot or two. It’s helped my little one with walking again. He was doing great then fell a few times and sort of stopped walking from one thing to another unsupported but he’s started again after wearing the Bombas for about 2 weeks.