There are a few directions you can go in choosing his first rifle. One thing to remember is you want one that will be comfortable for him to shoot so he'll enjoy it. Is he a big kid? Can he handle shooting a nine pound rifle? Most bolt actions are heavy and pack a good amount of recoil but they are often affordable. Semi autos on the other hand like an SKS or an M1 carbine are lighter but can get pricey.
At around $100 a Mosin Nagant 91/30 is the cheapest rifle available right now but may not be the best for a beginner due to some being finicky when it comes to a smooth cycling bolt. Mosin "sticky bolt syndrome" is a condition some Mosin rifles have where the shooter will sometimes have to whack the bolt with the palm of the hand to open the bolt because it starts to stick after a few rounds.
Everybody has their own idea on why some Mosins have a sticky bolt problem. Ammo casing differences like steel, bi-metal, brass, laquer coated casings, etc. defects in the rifle such as dirt/grease in the chamber or a burr from poor machining, headspace thats slightly out of spec, the list goes on.
I'm not saying you'll get a Mosin with this issue, just saying its a possibility and could easily turn a young shooter off.
Other options for bolt actions are Enfields and Mauser type rifles like Yugo M48s, 24/47s, and Russian capture K98s. Mauser actions are the smoothest out of all the affordable milsurp rifles and are easy to shoot. Both Enfields and most Mauser types will average around $200 to $300 depending on the model and condition of the rifle. Ammo for both is still available in surplus and modern production but 303 British for the Enfield can be a little hard to find and pricey sometimes.
Of course after reading these posts you can guess people are going to recomend what they like to shoot and of course I'm going to tell you to get an SKS.
Norinco models are at every gun show for under $250 but they are going up and so is 7.62x39 ammo so if you are thinking on getting one, get it soon and buy ammo in bulk like a sleeve or better yet a case. You'll spend money but the savings will be worth it and its not like you'll never use it, trust me.