Think about cork or a low pile carpet for a floor that is ok for office or gym.

I'm thinking hard wood stained to match as closely as possible to your current flooring.

3/4" gym mats for when you drop the weights.

Mats on the floor of a gym and hardwood for the space stained to match the rest of the hardwood . You get unfinished in the same wood as you already have and have it stained to match. BTW you need to roll up the mats when done working out each day they will discolor the floor .You also need to get the rollers on your office chair to be for hardwood .

You have THREE bedrooms. You are going hardwood in all?

No no no no no to this

Either get a sand on site floor, and stain to match existing hardwood in all three rooms

Or re carpet all three rooms in a very sturdy nylon. All the same carpet selection..

A bench and some free weights ( what POUNDS??) does not a "gym" make. A good carpet in nylon with pad beneath, a glass beneath your desk chair.

I would ask does anyone leave the house anymore, but a moot question it would seem : )