I would go with a wool rug. It's softer than jute or seagrass and not as difficult to clean as shag or fur. I'd avoid doing a stainguard, as the chemicals are toxic. Pick up a spray bottle of Nature's Miracle (usually found with pet supplies) for all the kid messes. Get an 8x10 to fill the space and to get the front feet of your furniture on it. We often push the coffee table up against the sofa for extra play space. Try ebay for discontinued styles from Pottery Barn and others. We got an 8x10 PB 100% wool rug through ebay for $300.