Carpet is always the cheapest cost. If budget rules, then that is what you can actually afford.

Carpet also hides some of the worst subfloors ever. Subfloors that will need extensive prep before any other type of flooring can be installed. That’s costly.

And you haven’t even talked materials. Or the big elephant in the room, labor. Labor is 2/3 of the cost of a job like this. Tile will end up being the most expensive up front choice, but it is a lifetime choice if done properly. Wood is second in cost for both up front cost and lifecycle low costs.

Vinyl and laminate are temporary choices that still require all of the prep labor. And a lot of the expensive install labor. But then you get to repeat that, as they are far from a lifetime flooring choice.

Dont hire a cheap hack. You’ll regret it. Hire wisely.

https://www.ceramictilefoundation.org/homeowners-guide-to-hiring-qualified-tile-installer