My kids have Kindle Fires and they're an excellent option. They play Minecraft on them, and Amazon has a lot of games & apps for free or low cost that are great for kids. I've installed a number of fun yet educational games that they like - for free - and it's a kindle, so tons of books.
Kindles also have FreeTime app for kids' use - you select which specific apps they can access, and you can set time limits for access. Works great for us!
Then, the best part, is the price. The 7" kindle is about $99.00. There's also a kid's version that is in a kid-proof case and comes with a replacement warranty - pretty sure it covers drops, falls, etc. That one is still under $150. There's also an 8" and a 10", and you can get with upgraded memory size. Larger memory is a good idea with a lot of games (with room still for books!).
Kindles run a customized version of Android. (I'm not an apple fan, so this is a big plus for me) I really would recommend the Kindle as a really good, safe, affordable option.