You should have builders risk and a separate liability policy while building. Once your build is complete, switch to your homeowners policy. If you have significant assets, buy an umbrella policy as well and keep it. It won't cost you much and will protect you if something happens beyond your policy limits. It's up to you how you purchase, whether direct or through a broker. There are advantages to both, really.

What are the odds of me going to a typical local insurance agent or broker and saying that I'm building a house can you help me understand "builders risk and liability policy while building" and them knowing exactly what I'm talking about? In other words, do I need to seek out a specialist agent/broker for dealing with my situation or should any of them know all about this type of situation?

Very good. Most insurers know what those policies are, they aren't rare. You don't need a specialized agent. Unless you find an agent or broker who isn't licensed to sell those types of policies. (IE you call a health insurance agent..)

We used (and still use) an American Family agent. It took all of about 2 minutes to set up our policies for our build. If you're worried, call around to a few brokers and see what they say. They'll search out the best agent or company for your needs.

Fidelity bonds on the build are also worth considering. We had one, and while (thankfully) we didn't need it, I recall a thread here a while back about a contractor/builder dying and leaving his clients in a bit of a pinch.