Kiddo wore knock off robeez from ebay when he first started walking. Once he started walking outside more, I got him some stride rites.
Barefoot is best for beginning walking but in winter obviously that's not always an option!
my DD started walking at 9.5 months and i was all worried about it too, especially over winter. but honestly barefoot IS best, and you'll probably end up taking the shoes off all the time anyway, or at least i did. so the kind of shoes really didn't matter much. soft soles, you can find stuff anywhere really. we didnt take her out in the snow that year, but if you want to, that's a different story.
for winter we LOVED these robeez boots with fur lining that my sister got for DD (also come in navy), i wouldn't have paid so much for shoes but omg i'm so glad she did cuz they were the BEST! they'd slide on so easily and kept her feet warm outside while i was carrying her to/from the car.
I got DS pedipeds:
I bought DS a couple pair on sale. They are usually around $30-35, but you can find some around $20.
I also got a couple from Target. My local Marshalls also had a good selection of shoes. GL!
I had DS barefoot or in socks or in Robeez until he had been walking for about 3 months and he was really stable enough to walk when we were out. Until then he occassionally walked outside or in a store in his Robeez. As long as they aren't waliking on rough pavement a lot the Robeez can take it.
After that we got him stride rites. I have been happy with them so far. They have good deals sometimes. The first 2 pairs i got buy 1 get one 50% off and the 3rd I got at 20% off.