How do I remove the Store and Support buttons from the header?  

You can "disable them" but that turns off the feature. The only way I've managed do this is to purchase and use CJ Menu. 

where do you disable them?

Option 1 - set permissions for the groups that you don't want to access the store / support

Option 2 - Applications > Commerce > Store / Support ( disable them ) nobody can use them (not even admin)

I sell banner ads with the store, but usually get business with a link in the footer. Having the store button in the header is a bit overkill for just that. 

in applications > click on the padlock choose the padlock on the Commerce and turn off Show in Navigation.

you can access it thru a link still.