All those floors are different. Shop around and buy some full-size samples. Decide from there.

I put some plain black 3/8" Amorim roll rubber in my garage.workout area recently. It's great but did have a little smell initially. It's not pretty or economical and most rubber floors I've seen cost more.

Why not vinyl plank or tile it also keeps the floor a bit warmer. Looks good and IMO is better than tubber tile

Not sure I would do the whole basement, but we did our laundry room with a roll.

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Rubber flooring (the real stuff) is some of the most expensive flooring we have. The highest level stuff is used in museums where a 6 hour day for a visitor is NORMAL (yes...6 hours in a museum is nothing to enthusiasts).

I just visited the Royal Tyrrell Museum in Drummheller Alberta (world class dinosaur museum). http://www.tyrrellmuseum.com/

The front page of the website shows a person standing on what looks like carpet. It is not. It is a 3/4" rubber floor. This stuff can be $15/sf and higher. Especially the high-end stuff that does NOT smell.

If you want a room for kids, carpet is your fastest, least expensive option. It reduces noise, it is warm and comfortable to sit on/play on and can easily accommodate furniture.

If you want economical/functional in a basement = carpet.

If you want museum level flooring = rubber (with the museum sized price tag).

And for those of us who are allergic to latex/rubber, the low-end stuff (made for residential areas) are a trip to the hospital waiting to happen.

I did not have an issue with the flooring at the Royal Tyrrell Museum...but then again they used the best of the best of the best of the best. No expense was spared in that place.

Most basement playrooms do not receive that type of financial attention.

Just a thought.. I spent my childhood with a giant unfinished basement. The concrete floor was fantastic for rollerskating, remote control cars, and anything else with wheels. It's also perfect for setting up train sets and ridiculous amounts of legos, among other things. But if you're putting in a trampoline or gymnastics equipment (higher injury risk), or just a cozy place to watch cartoons--that would all be different. What I'm saying is: Consider what you think "romping" might look like (and how it might change when they are 5, 10, 15...) before you decide on a floor.

Those walls look like a great opportunity to set the kids loose with some paint when they are a bit older.

I would finish most of the concrete with a floor epoxy (good if you want to use for storage or play), and a small space with replaceable carpet tiles for reading books, coloring, etc. Do you have smoke alarms installed? It would worry me to have a play space without an exit.

We used the colorful foam mat squares that interlock in our basement for our kids when they were younger. We also painted the walls white. It was an awesome setup. The kids are now in high school so we just finished the basement. In fact I have stacks of foam mats sitting in my living room! Here’s a picture of a small section. Our basement is approximately 1600 sq ft and we probably did this in just over half. My kids played basketball, softball, hockey, etc. They had a great time down there with their friends. I should mention that we wrapped poles with carpet.