Good surface for under child's backyard swing set?

If you don't want to use grass, I reccomend building an area around the swingset using landscape timbers and filling it with pea gravel. Put it to a depth of about 6 inches. This will absorb impact better than any other surface in case the kiddo takes a tumble.

You should be able to find the materials at Lowes or Home Depot, but I have no idea what you can expect to spend.

I think that no matter what surface type you use you will kill the grass underneath of it. Regardless, most people are using recycled rubber mulch-- its basically shredded rubber tires, it is clean and provides a forgiving surface should the little one happen to fall- you can get it from any home improvement store for a few dollars a bag since you are gong to be using it on a small scale.

Or if you are really concerned about the grass you could just place a few bags worht of sand at the foot of the slide, and then you are only killing 1 or 2 square feet of grass.

No matter what you're gonna put to some extent the grass under won't be able to grow. Since she's just one (1) year old just take a nice blanket while she's playing under your supervision. But when she gets older and graduate to the big swing you can use" Rubber" mulch made from recycled rubber material used in landscaping and walking trails. it might be pricey but last a lot longer. you can find this product at Lowe's and Home Depot.

Mulch

I think no matter what you put down, the grass will die. Peastone is recommended for daycares in Florida. I thought wood chips would be good but the kids will get splinters and I've heard some pressure treated wood has arsenic in it. (In case you decide to make your own wood chips, you won't want to use pressure treated wood leftovers)

I would suggest mulch for under a swingset/playground area.

Also, make it large enough to accomodate a larger swingset, when your daughter gets older

Use rubber mulch