Most Lego Mindstorms sets are designated for ages 8 and up, but there are a couple that are listed as more appropriate for 10 and up. Really, you will know your child best and will know whether it is appropriate for their level and abilities. Do not get something unrealistically above their level. It is never encouraging to set them up to do something that they will just fail at.
But, just like Legos themselves can be used at any age, Mindstorms is also perfectly acceptable to use by adults as well. IF you are just starting out in robotics, they are a great place to start with. You will learn how the pieces work together and what is needed to make a robot work. If you are unfamiliar with electronics, I say start here in order to get your feet wet.
They really will teach you the basics of robotics. Lego had gotten together with MIT in order to create the entire system, so you know that it has been built and designed by actual robotic engineers. There is actually an educational version that is used in schools that was designed by Tufts University that is focused more on the teaching aspects of things.
Anything to do with robotics is going to be expensive. You need metal parts and high quality parts. You cannot really cut corners in the world of robotics. Since it is all electronic, there are no cheap plastic substitutes. A robot is really a computer that you have built from scratch. It is programmed just like a computer and operates the same way. The difference is you see what it does on a very physical level instead of on a screen. Have you seen cheap computer parts? Not really. When it all adds up, it is all going to cost a lot of money. The advantage of the Mindstorms is that the parts are already put together in a package for you and you know that they are going to operate well together. Sometimes paying a little extra for something you know is going to work is worth it. Otherwise you could be hunting all over the place for parts, costing you more time and perhaps more money if you do not get the right parts to begin with.
Robots are used in every aspect of your daily life, you just probably do not realize it. Industrial robots have been constructing things for use for decades. They are incredibly useful. They can do the jobs too dangerous for people to do and do them endlessly until their parts break down and need to be replaced. It is amazing. And you can even get little robots to help you in your home. One of the most visual robots you can buy that is common is the Roomba vacuum. It cleans your house for you. Pretty cool.