You can use solid rift and quarter sawn solid wood floor, IMO, you don't really gain much with solid wood. With engineered products, you can use wider boards like Mirage's Sweet Memories Handcrafted White Oak R&Q that goes to 6.5" wide.

Yah...solid floors are possible but you need VERY narrow planks (3" or narrower) AND you need a whole home humidifier (possibly a dehumidifier as well depending on your location). The whole-home in floor radiant systems can dry out wood flooring VERY quickly. And dry wood shrinks. And shrinks. And if it gets TOO dry, it cracks and splits (aka. "checking").

To avoid these issues, you will need to pipe in humidity. Usually this is done through a traditional HVAC system through the vents....but if you do not HAVE vents, you will have a hard time getting the humidity levels stable throughout the home.

Engineered hardwood offers you a greater range of products (which are traditionally thinner) and greater choices of widths, but still require the humidity control.

Please find out how you will be able to maintain the humidity levels required for wood. This should be part of your home heating discussions with your contractor.

So is the veneer on the engineering flooring just decorative?

The veneer on engineered hardwood floors is THE HARDWOOD you are purchasing. So if you purchase "hickory" engineered, the top layer is hickory and the rest is often "something else".

Engineered hardwood is layered. These layers are put down using different directions. The different directions allow for more stability in difficult settings - like over in-floor radiant heat coils - but it doesn't absolve the homeowner from the "humidity requirements" inherent in all wood floors.

The different layers of wood that makes up the engineered flooring is what keep the floors stable using radiated heating, but the piece of hardwood on top is decorative. Correct?

hankws , look for an Engineered plank that has a wear layer at least 4mm thick. We have a helpful buyers guide here <- link