My preference would be to replace the carpet with the same wood and then refinish the whole floor (old and new) so it all matches. If you don't want to refinish the existing hardwood, then I would say don't try to "match" but rather do something totally different, either tile or new carpet. I'm not a fan of tile (too cold and hard, and echo-y in a room with a tv) so I'd do carpet, but I think I'm in the minority on Houzz about that.

I can't find a photo, but this gives you an example. Go with an oak floor but consider a darker stained accent inlay transition board at the doorways or between the two floors. This way the two floors will not be side by side to show a slight difference in color overall.

The best option is, of course, the same hardwood (same species, board width and cut) as what you have. If you do NOT want to redo everything, you don't have to. It won't look "right", but it can be done.

The important part is the species and plank match! Very, Very important. What you can do is add a stain to the "new" floor to give it a reason for being different. It isn't my favourite trick but it will "do" for now.

You will live with the two floors "as-is" until it is time to refinish the original floors. This is when you have ALL of the wood sanded and refinished at the same time. The species and plank match will become SUPER important at this stage.

My question becomes, how old is the finish on the original floors? You may have only a few years left on them before the NEED to be done. If that is the case, I would go ahead and do everything all at once...or wait another year or two and have the new hardwood installed at the same time that you want to refinish the existing hardwood.

Somewhere along the line, all the floors NEED to be refinished at the same time. There is no way around that (design wise). Find out how long that finish on the original has left to go and then make an informed, educated decision at that time.

We used this transition from hardwood to marble tile in a similar situation as yours. It turned out beautifully and added a visual divide between the areas making the space seem larger and more interesting.

The original finish is 25 years old and definitely needs redone, but my 3 small kids are preventing me from doing so...for now.
Thank you so much. You all have been very helpful!