What category do I use for concrete that we do charge the client for and what do I use for services from another contractor that I bill the client for?

When you pay for the concrete it is an expense, job materials expense or something like that

then you charge the customer using a service item

sub contractor payments need to post to an expense account that you have mapped to the 1099 for end of year reporting.  What expense account you use is up to you.  When you report income taxes sub contractor payments are posted to the tax form block titled non employee compensation, so that is the name of the expense account I use - just makes it easier at tax time IMO.