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Which floor system fits your slab?
Five questions. It will not tell you a price, and it cannot see your concrete, but it will tell you which route is worth looking at first and what still has to be checked on site.
Mechanical polishing looks like the right route
Your answers point at cutting and hardening the slab itself rather than putting something on top of it. That is the finish that wears best when the slab can take it. What your floor will actually look like depends on what is in that concrete, which a test grind settles.
Grind and seal is probably the sensible route
A full polish cuts deep enough to show the stone, and on a slab like yours that can expose more repair than you want. Grinding less and sealing gives you a finished floor without chasing a look the slab will not give up easily.
A polishable overlay is worth looking at
When a slab will not take a polish, an overlay puts a new polishable layer over it rather than replacing the floor. Sometimes that is the straight answer, and it is cheaper than it sounds compared with a tear out.
A coating probably suits this better than a polish
For this kind of traffic and wear, a resin coating is usually the more practical floor. It sits on top rather than being the slab, so it is a different maintenance story, and we will tell you which trade off you are making.
Start with a moisture test, not a finish
Damp spots, efflorescence or a coating that lifted all point at moisture coming up through the slab. That decides what will stick and what will fail, and no finish choice is worth making before it is measured. This is the one answer where guessing is expensive.
Your slab needs looking at before this question has an answer
Too much of this depends on what is actually under there. That is not a dodge: old adhesive, hidden repairs and how flat the floor is all change the answer, and none of it shows up in photos reliably.
What this is not
This is a starting point from five answers, not an inspection. Every one of these routes depends on what the slab shows once we are standing on it, and we would rather tell you that now than after you have chosen a finish.