Backyard Play Area

The best option would be the rubber mulch. It is made from recycled tires, & never needs to be replaced. Just mark the area, put down a landscaping cover (to prevent grass & weed growth), then level out the mulch.
Another option, that I actually use for my kids is the rubber mat squares. These are 18 inch squares that connect together. You can find them in gray or black anywhere exercise equipment is sold. Or, you can find it in toy stores & dept stores sold as "play mats", usually in various colors. This might be a good option for now since you will have 2 very young children. The mats are easy to clean off with a hose, & you don't need to worry about the kids "eating" it.
But, still let them play in the grass & dirt once in a while. It helps build their immune system.

first we created a boarder around the play area. I've seen it done with landscape timbers or just the rubber landscape boarder you can get at Home Depot. We put down landscape fabric then put down play mulch that our local landscaper tucked in. The mulch does break down after a few years and will need to be replenished. It's great not having to mow around the play area and it cushions the kids when they fall. It looks nice too.

We have had rubber mulch under our swing set for about 7 years now. We put it there just in case our then 2 year old, and the million other kids who still use the swing set today, ever got hurt. So far, no injuries, and we've never had to replace the mulch or have we had any mold issues, etc. We ordered our mulch from Close the Loop. At the time, the offered many different types and colors of mulch. The first few days, the kids were a little dirty from the mulch, but that soon stopped. This mulch is quick to dry after a rain. I would recommend this product.

We do not use anything around our swingset, etc. either but they do sell "rubber mulch" at Costco that people can use.

Good luck!

We have put up our swing set just last weekend, but it is not in its final spot yet, since that has to be landscaped first. Until then it is just on the lawn, and already now I can tell that the grass gets easily destroyed and muddy, especially under the swings. Our neighbors have one of those big wooden jungle gyms, and they put wood chips under it, which works great. You can get that even for free at you local green recycling yard (at least that's the case in White Plains). The wood chips dry very quickly after rain and there is no muddy built-up under the play area. The key is to put some kind of a frame around the edges, so that the wood chips don't spread throughout your whole yard. They used thin logs, which have to be put in properly though: dig a shallow trench into the ground and put them in, so they don't move around. Then secure them in place even more with some wooden stalks knocked into the ground, so nobody trips over them. This may sound labor intense, but believe me, our neighbors are really no big time handymen, and they did it all by themselves in not too much time.
Good luck and fun times in your backyard!

We have wood mulch under ours. We considered rubber mulch, but rubber mulch can be very expensive depending on the size of the area you're trying to cover. Also, it's not just the surface area. If it's going to act as a cushion, it needs to be a couple inches deep too.

Outdoor play area, you use grass. Why would you put some
sort of flooring down? The fun of being outside is
grass, flowers, and yes even mud.

We just have grass under ours. I never thought of using anything special for our own yard, although it's a good idea to not have to deal with mud! The school, and local parks around here use wood chips. There was a park we went to in another state that had rubber mulch, although the kids got extremely nasty when they played there. I think the rubber must have come from recycling old tires, and they apparently weren't washed before being mulched.

Honestly...I never even thought of special flooring. Except for the sand area, we just left the grass around our swing set and other little tyke stuff. Not fun mowing the lawn around it though! Curious to see what kind of responses you get. THe park near us uses rubber (tires I think. I know that Lowes/ Home Depot sells similar stuff. My kids have thankfully never hurt themselves in either surroundings. Best of everything!