The fewer changes in flooring in a home, the better.

Show a picture, but if you MUST split the project? An engineered hardwood in white oak, or a sand on site hardwood in oak, as both will allow add on and refinish up the road.

Better? Do it all and all at once.

All flooring needs to be planned and purchesed for the whole at least living space . Since this is a type of entry that is always tricky keep it simple same flooring on floor , stairs and the rooms connecting . . There IMO is no rush to do this one space at a time . We do need some pics posted here in a comment but you need to wait until you have a cohesive plan in place for all the changes you want to do.

I need new flooring on the stairs

What type of flooring is on the stairs and what is under that flooring?

It depends on your climate and style

Thank you everyone! The problem is that I don’t have a budget to all the floors right now. The stairs currently have carpet on them, which my cats have been using as a bathroom, so I’ve been ripping up the carpet as it gets gross. Maybe there’s something I could cover the steps with cheaply and temporarily until I have the budget to redo everything.

I have the same issue - I'm wanting to remove the carpeting on the stairs of my bi-level but the floring that is upstiars and downstairs is discontinued. Upstairs I have a medium toned LVP and downstairs in a brownish tile. Unsure what to do in the middle. Did you end up making a change or keeping things as is for now?