Dear Robbie,
I am in a really good place of having more inquiries than I can handle.  When someone contacts me, should I talk to them to explore what they are looking for  and then let them know about my availability or do I tell them this before I even talk to them?
Your Mentoree
Dear Mentoree,
Congratulations!  Your outstanding work and marketing activities have primed the pump. But we all know that consulting is a lumpy business.  Part of Disciplined Marketing is the willingness to focus your activities on your next key objective. In this case, it's not about getting business, but getting the right business.  It's also about operations, and being able to leverage yourself to best serve your clients and free up your time.
You definitely want to continue building relationships, even when you're busy. In fact, it's most critical to keep investing in marketing and sales when you are busy, because otherwise, when all the projects are complete, you might find yourself with a dry well.
Make the time to respond with thought and care to each prospect who inquires about your service.  You want to establish a relationship, and even if you can't help them right away, you might be able to introduce them to someone on your team, or to a peer.  Do your best to provide value to every prospect, even if you can't provide consulting services to them at this point.
When you have so much business that you have to turn some away, it's a good time to decide if you want to build out the operations to serve more clients (subs/partners etc) OR if you want to raise the bar on what you're willing to take on–raise your prices, turn away work that's not in your sweet spot etc.
It's great that you are thinking about these issues strategically. They will help your business to thrive!