there will probably be others along with good advice but ex is a drummer so i know a little bit.
i'd go with a full size kit if he's 9 (unless he's very small for his age)
Definitely buy second hand, new kits lose value as soon as you buy them and you will get a much better kit for your money second hand.
Stick with makes like Pearl, Yamaha, DW, Premier, Slingerland, Mapex, Gretsch.
Ex's first kit was a Pearl Export, pretty decent entry level kit and did him ten years of pretty hefty abuse, being lugged in and out of a van for gigs.
You need to factor in the cost of cymbals and hard-ware too. Buying second hand you'll get the shell pack (drums) and hardware (stands) but not all drummers sell on cymbals. Likewise the snare drum, these tend to be a personal item. So check carefully when you buy that you are getting exactly what you need.
Either get round some music shops (they often sell second-hand either in the shop or cards on a 'for sale' board), get in touch with your local college if they do a music course or your local youth club as lots of them run music projects now. The other good option is Ebay - but do your research first. Ex has picked up some pretty good bargains but he knows his stuff.