Hey there, even though I'm still relatively new here , I feel qualified to answer you questions.
First off, I believe that you mean the 3570k, not 3750k. And I'm wondering where you are able to purchase the 3570k without the HD4000 graphics, as this is integrated into the processor, and every chip comes with it. I think that you can rest assured that any 3570k you purchase will come with the HD 4000.
To answer your question about using a video card with the HD 4000 graphics, yes they will work together. In fact, it's nice to have at least basic integrated graphics on your processor in case your dedicated graphics card breaks on you. That way you will at least be able to keep using your pc, if not do intense gaming on it. To be honest with you, I've found the HD 4000 fine for my needs right now. It isn't good for anything other than older games on medium to high settings, but that's all I own right now anyway and I care more about the gameplay than graphics (mass effect 1 and 2 are amazing games). I support that choice on the motherboard also.
EDIT: Also, I would highly recommend putting your complete build up in the builds part of the forum to get recommendations from some of the experts here at Tom's. They can help you out with pricing and where to buy your parts, along with steering clear of any parts known to be low quality. Be prepared for the potential to be overwhelmed with information though. I spent weeks figuring out my build for my circumstances, but am thoroughly enjoying the results.
2nd Edit: just realized that I typed discrete instead of dedicated. fixed it.