Building your own home....oh, where do I start? We've been building our home for the last 10+ years, but that is because we are doing everything ourselves - probably the worst decision that we've made. But, on to your situation. First, a GC is not going to let you "pitch-in" for a reduction in cost, if anything they will add on because you'll be in their way. Fees are very location-specific, so you need to call around and see what the going price is per sq ft, and ask what that includes (granite or tile counter tops, hardwood or tile floors, hardscape, softscape, deck, porch, permits, architect designs, etc.).
Unless you are construction savvy (I mean structurally, not just, Hey, I've laid tile before, I know construction!), you will be relying a lot on your Builder, so make sure you go with someone who has a stellar reputation and is not the cheapest. Be prepared for change orders - what ever they quote you, be prepared for 10 - 20% more - especially if you need to pull in any utilities, there are always surprises. Be prepared that it is going to take longer than expected, especially depending on how crazy the weather is in your area. Also, you'll more than likely have to get a construction loan which is at a higher rate than a normal mortgage and then convert it once you get your permit for occupancy - so plan on more carrying costs with the construction loan (and additional points).
So, it's unclear if you plan on being the GC or not - if you think you are, think again. You need to know how a house is put together and where one trade discipline starts and stops - you need to know if the plumbers lay the pipe at the right pitch, you need to check that the framers build to your plan to the inch or you'll have problems, you need to know if they use the right weather wrapping when installing your windows, etc., etc. The important thing is not knowing how to build a house, but how to recognize when someone is fucking up.
My DH has a lot of construction experience and exceptional mechanical aptitude and he was constantly after the trade guys (he was a trade guy!) to do their jobs, show up when they said, and build to code and spec - it was fun and frustrating all at the same time! But unless you're particularly construction savvy, I'd strongly suggest against being your own GC.