I desperately need to fix my oak floors.
If you are confident enough to do this yourself, you'll have to start by renting a floor sander. Get the kind with 4 smaller cricular pads... DON'T get a drum sander. They are difficult to use and can realy mess up a floor if used incorrectly. The type w 4 pads usually has a dust collention system attached (very convenient). After sanding the finish is up to your preference as to color. Make sure to end w a floor grade polyeurethane (get one made for gyms floors).
You also may have to trim down the doors a bit if you raise the level of the floor too much.) Your oak floor actually looks great and just needs to be refinished. The wood looks nice and tight (no gaps or visible defects) and has a nice grain pattern. Have you considered just refinishing the floor? It would involve sanding the floor down to bare wood and applying a new finish. I would cost next to nothing compared to installing a new cherry floor (though I also really like the look of the brazilian cherry; for some reason the HGTV link you posted didn't work, I just did a search for Brazilian Cherry on HGTV and found the Classic Tuscan Kitchen episode). Sanding a floor is messy work and can be a bit tricky if you use a drum sander. A drum sander can oversand a floor quite quickly but works great in the hands of a pro. You also need to cover everything as wood dust will get everywhere. There are other types of sanders you can rent (I've used a 4 disc sander to refinish a floor) that are not as aggressive as a drum sander but they do take longer to sand. Even hiring a pro to sand and refinish the floor would most likely be much less expensive than buying new wood. But if you have the coin and are set on switching to cherry you can certainly install a new floor over the old floor provided the old floor is in sound condition (not loose and warped).