You can put some thick plastic or rubber over the ground in your crawl space. You can get the ceiling of your crawlspace sealed with spray foam. Your climate matters. Are you in a rainy or a dry area? Do you have gutters, downspouts and drainage moving rain away from your crawl space? Are you on the bottom of a slope so water flows down to your crawlspace? Are you on the top of a slope, so water flows away from your crawlspace?

It's very hard to answer the question without particulars.

Thanks. We are at the bottom of a slope but have invested in a drainage system, so the crawlspace is dry. Still, it is a rainy climate so things are generally humid.

There are many factors that could affect the performance of your floor. I live in an area with many old frame houses with crawl space. Most are performing fine. The things to look at are your indoor and outdoor temperature and humidity, and whether they can be transferred via the crawl space. Over time, many houses have been updated with better a/c along with doors and windows that seal better. This can lead to houses that are a cold box that lacks insulation. If you have a cold floor and subfloor, a high humidity condition in your crawl space could lead to condensation. In Florida, that could easily lead to cupping, but other locales might not have the same issue. Adding something to seal the ground should NOT be done without considering the consequences. Companies that provide that service also usually have a comprehensive plan that addresses those consequences. That said, you probably don't need to cover the ground.

For a first step I recommend buying a thermo-hygrometer with remote sensors. I'd use a minimum of three, one indoors, one outdoors and one under the house. If you find that the crawl space has too much moisture, then insulating the underside of your subfloor is a good idea. I'm a fan of spray foam, but some may disagree.

There's not much you can do inside other than using a moisture retarder like Aquabar. Using a barrier between the subfloor and floor could have consequences. Aquabar allows moisture to pass through, but at a reduced rate.

As Sigrid noted above, more information is required to plot the best course.

Engineered hardwood plank flooring is a common choice today. You can get a stable product in a width of up to 11 inches that shows off the structure and beauty of the wood you choose. Placing 10mil plastic over the ground in your crawlspace will help reduce humidity swings that could affect the flooring. Pea gravel over the plastic helps protect it when you move around in the crawlspace.

You need to make sure there is good ventilation and that no wood comes in contact with moisture/condensation. The wood gets wet and will wick moisture up towards the hardwood.

If, you spray foam, do not just spray foam the cavities. You will need to spray over all wood material with closed cell foam Also, the joist needs to be a minimum of 18" away from soil.

A cheaper option is to install 2" xps faom board underneath. Cover all the joist and spray foam any gaps. The foam will stop moisture from migrating up. There will be a lot of condensation dripping off of it.

Very important that there is no wood touching any soil. Moisture will wick up.

A narrow hardwood floor won't have much opportunity to cup with changes in humidity. If you acclimate the wood, and use silicon paper or felt, your floor should be fine. You should also lay down some polyethylene over dirt in basement and run a dehumidifier.