"What do need to know about water quality?"

Get your water tested by an independent lab (not by a vendor of treatment). A potable water test will be 40-50 bucks.

"Do we have the water tested once the well is drilled?"

Yes, and periodically henceforth. The depth of the well has some effect on quality, deeper= better quality, with trade-offs in increased pump horsepower.

It shouldn't be hard to find a test lab in your area. The driller should know a source.

A water test will tell what sort of treatment is required; where you are, water is usually acid and may require neutralizing.

Whole house filters from a big box store are not a good idea.

Some in my area build and then drill the well. I do not think that is good procedure. For required separation of well, septic, boundaries and house on my site plan, the area for the well was within an area 20 x 60. After having the soil approved for the septic, the well was next. Without those, the build would be useless. Now tests of the water are mandated, but treatment is not.

When we built our house in "the country" our builder told us about the well drilling businesses in the area. We had a couple of them bid the job and had the well drilled about one year before we built the house. We had built a shop building on the property a year or so before. Anyway, the guy that drilled the well was able to tell us about the area and that we would more than likely need a water softener in the house as there was a lot of calcium in the area. So, after we built the house we had our water tested and installed a water softener system.