[JavaBrewer]

I'm not eager to be the first to suggest this...but for your needs I would seriously consider a used Mac Mini. A quick browse on Craigs list found a few in the $300 range. With Mac OS you don't have nearly as many concerns about internet security issues and general malware. Sure it's not 100% but then nothing is. Apple puts out good products and I'll bet a good condition used Mini will last as long (or longer) than the Dell you linked. If they outgrow the Mini - move it to the kitchen or garage for a simple internet access point.

Of course you did mention games...so if that is a realistic desire then none of the systems discussed so far are worthy. PC games require hefty graphics cards and memory.

Best of luck.