Unless this is one huge houes $14,000 is way to high. Sounds like someone for some reason did not want the job and bid high.
You say basement in one sentance, then talk about a crawl space in another. Which is it?
If the crawl space is lower then the outside grade then it will always be wet because water is going to seek any low spots.
Filling with sand to raise the inside grade then using a 6 mil black plastic vaper barrier held in place with insulation ties bent in half is the way to go.
Any house has mold and mildew growing under it to some extent, not sure why you would want that air inside the house.
Working gutters, no mulch piled up againt the foundation, grade sloping away from the foundation will all help.
Where all stupid, just in different subjects.