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??