[architype]

Another alternative is carpet tiles or squares. They are adhesive backed, (peel and stick), and easy to install. They are extremely durable and tend to have a short nap. This would be good for the fitness equipment since a deeper nap will show compression marks.
They are about 18" x 18" or 24" x 24" and can be installed over the old floor tiles as long as they are still tight and not peeling or cracking and coming loose.
They are also easy to pull up and replace if you need to in high traffic areas. Almost all airports use carpet tile now for this reason. You can install them yourself.
You can also create easy patterns with them or border the room in one color and use another color for the center.
You still might want to consider using the snap together rubber tiles for better impact resistance and comfort in the areas where you will have weights and exercise equipment. They can be put down right over the carpet tiles.
Check carpet suppliers in your area that deal with commercial applications.

P.S.: Just did a quick check online and Lowes carries several types at different price points.