Hi,
I would recommend using 'brand or product':
1. Only a couple of categories can be 'tagged' by other business pages. These are 'Artist, Band or Public Figure' and 'Brand and Products'. Pages classified as 'Local businesses' cannot be tagged by other businesses.
Tagging can be helpful in spreading the word about your business.
E.g. We feature one shop on fb.com/OrangeTwig daily. If we are able to tag this shop, it allows all our visitors to directly click through to it.
2. Select Local Business or Place only if you have a physical storefront that you want to drive traffic to. Facebook will automatically turn your Page into a Place as well. And you don’t want people coming to “check in” to your home office!
Most companies who sell both online and offline tend to choose 'Brand or Product'.