LH Savage Axis Youth in .223, .243, or 7-08, all around $280 from Buds. Throw in a transfer fee and you're still under $300, leaving plenty for a decent scope.
Much as I'm not a fan of the current trend of ultra cheap rifles, they do serve a purpose. This way, if the kid decides he doesn't like hunting, or shooting, or if he just outgrows it, you can send it on down the road. Even at a 30% loss you're still out less than the cost of a tank of gas.
As for those who recommend shooting a RH gun wrong handed, it's not just ergonomics but safety as well. First off, I challenge any lefty to shoot a quality LH rifle while exhibiting proper bolt manipulation and still honestly state that they prefer a RH gun. Won't happen. From the bench is one thing, but in the field, from field positions is a whole other ball game.
Also, as a LH shooter, I won't shoot a RH gun anymore because I value my eyesight too much. A ruptured case, or even just a pierced primer vents gas out of the action on the bolt side. In a properly fitted rifle, this should be away from your face. A lefty shooter with a RH gun will get a snoot full in the event of a catastrophic case failure.