Wood flooring and Heavy Wheel Chair

Just dealing with the matting question, I would assume regular matting would be ok, you will just need a lot of it. Assuming you will have one, I would keep the outside ramp clean, then have a commercial-quality welcome mat outside the door, and another two inside. (Like, the 3'x5' or so ones. Your goal is that the wheels have to make at least 1 complete revolution before leaving the mats.)

It may also be prudent (depending on your house) to have a different flooring for the area around the door, designed for higher wear.

Bamboo's a good choice. However there needs to be a much larger (1 to 2-inches) shrink & expand perimeter gap & subsequent baseboard shoe molding. It moves quite a lot.

If there's any ramp, even just a threshold one, then the best choice would be to go to a grating surface rather than the solid or plank options. Debris will then be handled outside.

If not, then the below mat is in the Home Improvement stores (Home Depot's website in this case) and is Cast Aluminum. Expensive & small, but 2 or three could be welded or hinged together to catch & hold debris. Or, of course any Open Grid type of matting, but many of those are soft rubber & might be difficult to traverse.

There is disagreement here, what you think is best for you. Occupational therapist recommends wood, laminate for easy clean, I prefer carpet it's softer and warmer. Consult the wheelchair user, they could have a preference for a good reason. A wheelchair does not mean mindless, sorry to be blunt but I use a wheelchair and know how it is. I prefer carpet in case I fall transferring, it hurts less.