You don't provide information necessary to give much assistance. Is the space already finished and needing a remodel or will everything be new build? How will the space be used - you mention egress window so are sleeping quarters being planned? Bathroom, office or other needs?

What I'm getting to is that you need a plan, even before you contact a contractor. All you need is a tape measure, some graph paper and a pencil with an eraser. Draw the area to scale, then add features you want. Keep in mind walls are 4.5" thick and that becomes alot of lost area. When you're uncertain of something, place masking tape on the floor to better visualize a room. Any time you invest doing your own planning will save you $$$'s and give a result you will be happy with. No contractor can imagine your desired usage for you. Someone once told me, If you can draw it, you can build it."

After you get the basic plan, professional assistance can guide you on insulation, flood control, electrical, plumbing, HVAC etc. based on existing systems and your needs. Your local building department probably has a pass-out with basic critera with which your build must comply. Talk with them too, you won't need a permit to create your plan.

I'm linking photos of our basement. It is all DIY, done in phases over 5 consecutive winters. We began with a plan which is posted too.

Hope this helps you begin. Best of luck.

Here is a link that might be useful: Basement Photos

I like the previous suggestion of starting with a tape measure and paper. Perhaps some thought as to how you want to use this space.

As for the contractor...if I understand you correctly you want to use his expertise in order to design your basement and then do the work yourself? I think want you might want is a designer, then the working relationship will be clearly defined.