Refinishing is a fraction of the cost of replacing. I had all the oak floors in my 1939 fixer refinished. When the old stain is removed, you'll have the same very light "like new" wood. Then, choose your stain to have applied to your floors.

Yeah, that travertine look is a bit dated. Not bad, but just yesterday. I just found a very convincing bluestone look in porcelain. I’m getting the darkest one, but there are 4 color ways. I am also a huge fan of Saltillo and cement tiles. Cement tiles can be laid out and bordered to look like a rug, and come in solids too. They have a very distinct feel underfoot. (There are caveats with those kind of tiles, though - installing them can be tricky.) https://www.ceramictileworksmn.com/chamonix/

What city or part of the country do you live in? The real estate market is so hot in most places now, and if this is the case where you live, I would not invest in putting in new floors for resale. Clean the floors, patch the floors, do some faux blending of touch up wood stain, and use throw rugs carefully. Also, ask the advice of a realtor about whether that is where you should be spending your money. We did this with our floors recently. Our wood floors were in really, really bad condition throughout the entire house. I patched, used wood stain pen, had a few planks patched in, and really great rugs on facebook marketplace. I carefully staged our house in a way that would draw your eyes up. Our house got four offers in one day on the market for almost 10% above asking price and waived home inspection. Meanwhile, the house two doors down was for sale at the same time, sat for 8 weeks and went to 10% less than listing price. Their floors were refinished and much nicer than mine.

Red oak never looks like white oak. It always has a pink undertone, even when chemically manipulated. Expensively manipulating a product to try to make it something it is not will cost more than full replacement with white oak. White oak is a premium choice, and you should be prepared for the entire project to be in the upper end of costs.