That's probably sheet vinyl. It is an EXCELLENT option in a rental. It is relatively cheap, durable, water proof and easy to install/replace as needed. I would do this for the kitchen and baths. I would replace carpet with carpet. It looks REALLY WEIRD if you use a 'stone look' product in an area normally reserved for wood or carpet. Like REALLY weird. So weird your renters will know you are cheaping out on them. Your counter tops are laminate. You have a small kitchen with nice (but basic) cabinetry. You have carpets in the living areas (what about the bedrooms). I would NOT put in expensive hardwoods. They will not increase the value you can ask for as rental income. To increase the rental income you must have real stone counters (although I'm a fan of laminate counters...they will out last several owners). You must have a SINGLE floor throughout the home, etc, etc, etc. I'm going to guess you will have a moderate income rental on your hands. I would recarpet the carpeted areas. I would reinstall updated sheet vinyl in the kitchen/wet areas. And expect to have those items replaced every few renters (every 7 years). Yes hardwoods can be sanded down and refinished...but that normally happens every 25 years...not every 7 years. If a hardwood floor is ruined/damaged to the point of full sand/refinish, you probably have to sue your renter (good luck with that!) to recoup the costs. A full sand/refinish costs $5/sf. It takes 3-4 days for the procedure and then ANOTHER 10-20 days for the floors to CURE. That means rental income lost for an entire month AND you have to pay for refinishing your hardwoods. You will lose money AND lose income. Best to stick with stuff that can be ripped out and replaced in a single day. Carpet and sheet vinyl will do the trick for most rental units that rank as modest or moderate income renters.

I think you can't ever go wrong with white blinds. Especially if they are high quality custom ones, they will be around longer than your current color scheme.

Your inspiration photo is handsome...but it has a much lighter floor and much lighter walls. And the light filled VAULT that highlights the wood is something you are missing. If you attempt a match like your the inspiration you are going to create a very dark looking space. The oak is very 'heavy'. That's a lot of trim that will be stained. And to get it to look good, you will have to go dark. Not medium....dark. Your floors are quite dark (we rank them as 'dark') which means your tone on tone match is going to be dark. Are you leaving the houses trim WHITE? I would keep the trim and the stringers white. I like the idea of the hand rail matching or being DARKER than the flooring. Your newel posts could be white - same as the trim. Or BLACK. Just be aware you have Red Oak. The red is going to be tough to get away from. You can use Jacobean to get rid of the red AND to darken the stain. But be careful with all the heavy trim work on the stairs. They are going to be powerful if you go dark. It will look very, very heavy.

If you want to leave the wood panel and floors and stone fireplace, then go for it with Arts + Crafts, like wall covering and fabric from William Morris or Bradbury. Your room could look amazing. Do some research on Morris and Bradbury to get a feel for the luscious "camp" style. William Morris: https://www.designerwallcoverings.com/pages/history-of-william-morris Bradbury: https://www.google.com/search?sxsrf=ALeKk01jBdcLiOt41ucOYb7mDmxEXTpY4Q:1602649928391&source=univ&tbm=isch&q=bradbury+wallpaper&sa=X&ved=2ahUKEwiz-LidoLPsAhWoiOAKHUO3AGcQjJkEegQIDhAB&biw=1257&bih=978