You don't mention the age of your kid, that might be a big missing point.
Depending on the age, i'd follow different routes :
6-10 : the basic (red) set is fine, you'll find a lot of adventures by searching a bit on the internet. As time goes, you'll get to the "advanced" and "expert" sets (blue and green). most of the old modules have been re-edited for almost nothing. If you have a printer, pdf is your friend (it's cheap). Also you might want to find a few of these "be-the-hero" books, look in "used" bookstores, they're great introductions to roleplaying and fantasy settings, and this way your kid feels he does things by himself.
11-13 : basic is just a bit... basic, kid may want a bit more challenge, a bit more options. Either you go the 2nd edition way, still easy to play, lots of cheap books on ebay, i'd say find the forgotten realms set and buy the corresponding novels as an aside (it's great reading an epic novel and visiting the same places with your character)
14-16 : forget the basics, your kid is seeing everyday MMORPG players, computer RPG players, you need diversity, lots of options and real scale roleplaying. Go fot he 3.5 edition. the rules are free on the internet (www.d20srd.org) and by cruising the net you'll find the biggest free ressources available (settings, scenarios, etc.). Also with 4th ed coming, you may find great discount prices on 3.5 books (they sell for less than 15$ apiece right now)
If price is really a big matter, google is your best friend, you'll find nice free things for each and every edition there is. Otherwise, ebay is a good source, there are also very good sites which offer used books for a nice price. Internationaly-wise i can't help, but in france we have "ludikbazar" where you can find modules and scenarios for as cheap as 5$ apiece.