as long as you are not putting a machine into the stream bed and disturbing it directly its not a big deal unless there is some sort of fine print that the others are talking about that you need to get a wetlands agency envolved.
One thing that can help you determine what you're getting into is having a core sample taken of the property. it will tell you soil type, groundwater and rock depth.
if some rocks are big enough you might need controlled blasting. if your basement is below the stream bed grade wise, you would likely have to be pumping water 24/7 during the construction part. im not sure how well a poured concrete wall with the waterproofing on the outside will stand up to the water, but of course it would be better than a block basement. builders would reccomend under drains to drain the water. the best way to do this is mechanically, without a pump or you could still wind up pumping water 24/7 after construction is complete. Then if you have a power outage your basement will flood.
In reguards to flood plains and flood insurance. If its in the area then you may import good soil or clay to be compacted for a building pad. Have them build it up enough to get you above the elevation thats considered the floodplain, then all that is a null concept after that. Plus if the elevations work out, it could keep your basement out of the rock.
You dont know untill you get a core sample.