Wow, coming up (or down??) in the world with a basement, eh??
I have seen a number of home dojos. Here is a worst-case scenario that I learned aikido on: concrete floor with a shag carpet and carpet pad. I earned a separated shoulder on that floor!
The good news is that hi-tech comes to the rescue in the nineties. I highly recommend a type of interlocking spongy tile sold by many of the martial art houses (Century, Kwon, etc). This stuff isn't exactly cheap but it has a number of advantages that really make it absolutely perfect for basement dojos:
1) It comes in about 40 inch square pieces (varies by manufacturer) that fit together. The individual pieces can be trimmed to fit against the wall, around ceiling supports, etc. You can actually get them in different colors if you have a dojo floor scheme in mind.
2) The tiles can be gotten in different thicknesses so you can get anything from a mild cushion to a virtually standard judo or aikido grade shock absorption ability.
3) All of them have some degree of shock absorption that is actually better than the standard wooden floor. This actually makes it possible to PRACTICE all those throws that most Uechi-ka never practice (because they don't know how and/or they can't fall on hard surfaces). Thus one might argue that this is a better "standard" for Uechi Ryu than the traditional wooden floor.
4) Sooner or later, all basements leak. Period. What happens to your carpet floor? Your precious wooden floor? Yes, you can come up with a number of neat options to redirect water from walls and corners if the worst imaginable happens, but even that isn't 100% foolproof. Last winter with El Nino rains, I actually had dampness seeping up from the tiny cracks in the FLOOR of my concrete basement floor. Well if your floor ends up with water on it for a few days (or more), you can just pull the tiles apart, wipe them with a little bleach in water, put it back together after things dry, and you are back in business!
By the way, you have seen such floors, Josh. Mark Roscoe had such a floor in his old dojo where you took your shodan test. There was another similar floor at the Maryland dojo in our Mid-Atlantic regional where Sensei Spencer was guest.
A word of advice - shop around and haggle. And ask around about the quality of various mats. I get the impression that they are not all created equal. But anyhow I see them on sale in various catalogues. And some of the companies suggest that you can haggle if you order a large quantity. But most definitely mooch off of someone's discounted dojo account (it's about time you got your own!!).
Also ask around about tricks to keep basement floors dry.