I have a 13-year old who I started fly fishing when he was about 6 or 7. I find that an 8 - 81/2 foot rod suits him quite well at his age, not that a 9 foot rod would not be good, but it all depends on the strength and leverage.
A good place to start would be with a 5 or 6wt rod. The wt refers to the Line weight. You can fish trout and panfish with a 5 or 6 wt easily. I would probably go with a 6 wt as it will give you a bit more latitude when fishing different species and will help when you cast larger flies and plugs.
As for the cost of a set-up like this you can probably get a nice little outfit for under 200$ for a rod and a reel. No need to spend a ton of money right away. Give yourselves a bit of time to get into the sport and then the sky is the limit in terms of pricing and doo dads you can buy.
You may want to consider a good pair of waders to go along with the rod and reel as comfort is key when fishing. If you can wet wade (no waders - just wading in the water in jeans) then that is fine too, although you want to make sure that your footwear is proper for the task. This means that you want to get some footwear with FELT soles on them to prevent you and your Son from falling into the river!
Cabella's, Bass Pro shops and any other retail chain have decent gear for a good price, although I am the sort of guy who likes to support smaller shops that will give me good advice and ongoing service. That is not to say that the bigger guys cannot offer that, it is just my preference to do business with locals.
Once you and your son get geared up, drop me a private message and I will send you down some flies from Quebec. I have TONS and TONS of flies that I will never use and knowing they will go to two new anglers, I will be happy to send you a selection to get you started if you want.
Fathers and sons who fish together often form a very special bond that cannot be duplicated with other activities. I wish you both the best and many years of angling together.
Independent Salmon & Trout guide