It is cheapest to go with slab, then crawl space then basement. Basement may allow future space for expansion and are common in my market. Out west or in areas of high water tables they are less common. (expense is related to costs of excavating, water proofing, radon remediation...)
The foundation are the pilings and walls that hold up the house...the crawl space is the open area in between the foundation. Hope that makes sense. You can Google "Parts of a house" and look at diagrams.