There's no formula, but given that the floor is a much larger area that will have a bigger impact on the look of the space. Ideally, you pick everything before you actually start work on anything.

Paint is infinitely variable. You can pick that last. Pick first the product that comes in the least options. Get sample to view in your space with your light. And leds come in different whites from warm to bright stark.

There is no reason not to have ONE flooring in the basement. ( possible exception of course, a bath). There's no reason to carpet a guest bedroom in the basement, area rugs are plentiful.

Pick a flooring you love, engineered hardwood, or LVP. Pick the cabinetry, Ikea in conjunction with the flooring.

Then pick a counter top with those finishes in hand, at a stone source local to you.

If you select a flooring? You buy a single box before loading in the full quantity, and you are best with a local source.

After that? Counter tops, and finally? Paint!

You never, ever, begin with paint.

No gray in any LVP. please.

"Home entertainment" need not be more than a great media cabinet and a smart tv. No need to match to a kitchen cabinet finish : )

In general pick the materials and finishes for which you have the least options first. There are maybe a few flooring or countertop options that you like, and when those are chosen there's still probably dozens of paint colors even within the silver-grey family from which you could choose one which works best.

I think LVP is a great product for basements, but if you're replacing carpeting, be aware that LVP requires a flat floor (within a particular tolerance, consult the manufacturer). Carpet doesn't care if the floor is wavy. We had to have leveling compound applied in some areas to reduce the level changes before LVP was installed in our basement. As far as which to choose first, flooring first, then cabinets and countertop. Paint is always last because there are so many options. You can keep your chosen color in mind while you're looking, but be flexible, you may end up having to change the wall color slightly at the end to get the right color to complement the other elements. I had furniture already that I wanted to keep using when we chose the LVP, so that's what drove the flooring choice for us. The existing carpet (which was over ten years old, chosen by the previous owners) had a noticeable worn in traffic pattern. LVP won't do that, which is why I changed to that product. I've had it four years now. One of our former cats christened it. It's easier to clean up than carpet. Still glad I chose LVP.