My son 10.5 months, is starting to stand and walk around the furniture. Should he be wearing shoes or is bare feet best?

Barefoot. He may trip wearing shoes. And he'll have have better control barefoot.
Keep him barefoot. Keep him barefoot for him to develop balance and for his feet to learn how to "grip" properly. This is the most natural way for his feet to develop. Keep in mind that babies/toddler feet are still developing. Shoes should be worn if you go outside in order to protect from injury. In the house keep him barefoot or wear socks.
Shoes. In my opinion he should be wearing shoes to protect his feet from injury.
Skids. There are rubber soled socks available for any of these kids that protect the feet from the cold but do not add weight/restrict the feet as it grows.Simple soft moccasins or something similar can be used outdoors. Barefoot is fine also if it is warm.SHoes do not help a kid learn to walk & may increase their risk of falls/head injury.