However, when it comes to the grade of skateboard to buy, you certainly don't need to spend the money on a full scale pro grade skateboard. You can if you want to, and it's not a bad idea, but most young skaters won't really benefit from a full pro-grade skateboard.
So, if you'd like to save a little, there are several brands for young skaters out there. Check out our Beginner's Skateboard Buying Guide - this one focuses on kids and children's skateboards. Lower on the page, you'll see several different brand options that are still good enough quality, but cost less than pro grade skateboards.
Please, for the love of your child, do NOT buy a skateboard from some massive department store, like Walmart. Those generic skateboards aren't good quality, and will give your kid a bad experience. Just don't do it.
As far as the skateboard size goes, just get a smaller size of a full size skateboard. The width will be around 7 inches, and that should be OK. For the best experience, let your kid pick out a board that they like the graphics on. This might seem petty, but the graphics on the skateboard are strangely important to a skater.
One final word on pads - make sure you get a skateboard helmet. After that, you can get him or her elbow pads, too. Knee pads and wrist guards can also help. Beyond that, you should be fine. Termite, and other brands, make skateboard pad packs for kids. For more info, read the Skateboard Safety article.
That should be a great setup for your kid - have fun!