Even without knowing the kind of wood or condition, I can't imagine replacing wood flooring in an 1890 home. In my opinion, the value is in the original material. If the floor is in good condition, it may not need sanding at all; a screening and recoat might be all that's necessary and the patina would be retained. There are many threads on this topic, try searching the Old House forum. I live in a converted schoolhouse built in 1890. The fir floors had been covered with layers of linoleum, glue, paint ... they were a mess.. but looked awesome after refinishing. That was years ago and I'm planning to have them screened soon (aka buff and recoat.) What kind of wood is it? Do you have photos?

Sorry but these are as suspected. They are dry and the finish is VERY thin. The top photo (with crayons) are starting to show the effects of the purplish/black staining from the iron in dirt. I would say it started many years ago. These are in serious need of a full sand and refinish as quickly as you can. I would NOT do this piece-meal. It will cost you MORE and will be extremely aggravating to move your furniture many many many times. And have to live with "cure times" on multiple occasions and even the harsh chemical smell if you work with traditional oil based finishes (the stuff that makes your headache for 30+ days). Doing this all at once gets everything out of the way and all the pain dealt with in one fell swoop. And some of these finishes require you to be out of the house for more than a week (not including the 3-4 days you MUST be out of the way while the work is being done). Now imagine having to do that 3-5 times in one year. Ouch. Not my idea of fun. Seriously reconsider your decision to do this one room at a time. The floors are well past their due date for a refinish. Doing them all at once makes sense temporally and financially.

IMO all the floors should be the same color. Post a picture of the original floors and the color you want to restain

If you insist on the lighter flooring, then I would go with the slightly darker version (the one on the left in the last photo). Are you keeping the brick? If you are, the slightly darker wood floors are a better compliment than the super light wood. If you are removing the brick and rebuilding the stairs, then you will want to find out if either of the vinyl floors have stair treads and nosing available. People who have used vinyl that does NOT have treads/nosing found their BIGGEST headache comes from trying to find a solution to this problem. As for your darker wood floors, they look (just one photo with one chip out of the wood) like they could be ready for a sand/refinish. If they are, I HIGHLY recommend doing the hardwood FIRST...and then choosing the fake-wood look product for the den. You might find a good colour match can be had if your red oak hardwoods can be sanded and refinished as 'raw' = the colour of the planks you want to use. How old are your hardwood floors? If the finish is very close to 20 years old, they are ready for a full sand/refinish. It is always advisable to figure out the BIG ticket item before you try to figure out a small ticket item. And if you are refinishing the hardwood, why not add more of the same??