Russ - glad to hear you are considering an upgrade. Basically, you have a few options right now. I would not suggest keeping them in the bowl any longer because of the issues with oxygenation, and the fact that it would be very hard to attach most conventional filters. However, when you get the tank, you have a few things to consider. A 10 gallon set-up will be sufficient for a short while, but is not a long-term solution. Commons grow very rapidly with the proper space and diet, so what will very probably happen is that you will spend at least $30-40 on a 10 gallon set-up (which would mean a tank, hood, filter, and bubbler), only to have to buy a 30g (minimum!) tank somewhere down the road. Now, I understand that it is a pain to have a giant tank for small fish, but financially, buying the final tank right off the bat is a better option. I know that AGA sells some value set-ups for relatively cheap. Even the 55g tank with filter, hood, etc. only costs $158 at Petsmart; that is a real value, because many filters alone for a tank that size cost at least that much! So, you could "shop around" at stores that carry the AGA Value tanks - Wallmart, Petsmart, Petco, and Pet Supplies Plus to name a few. I believe they come in 10, 29, and 55, all for very reasonable prices.
In short? You basically have the option of continually buying upgrades as the fish outgrow thier tanks - which in the mean time may stress the fish due to gradually building waste levels as they grow - or you could buy the final tank size and cope with a very empty looking tank with two very little fish in it for the year or so it'll take them to start getting massive. Depending on your priorities - space economy v. financial economy - you should know what will work better for you overall. I personally wish I'd just gone ahead and bought the 75g for my goldfish; I started out with a 5g

for about $29 (well, they were technically my mom's back then), then had to pay about $75 for a 30g setup, and now have paid an embarassing amount of money for a 75g setup! If I had just bought, say, that AGA 55g for $158 to start with, I'd have a lot more money and much fewer problems along the way.
So, have I scared you enough about goldfish husbandry yet?
You know, another option if you are not able to afford or accomodate such large tanks would be to explain to your son why goldfish aren't right for your family and return them to the store, stressing to him the importance of why researching a species before buying it is important, and why it is right to surrender a pet you can not care for. Then, you could get a small set-up and get a fish like a betta; kids love bettas because they come in fun colors and have plenty of "attitude." You could get a Minibow 5 at Wallmart for I think around $30, which comes with a hood, light, and filter (not to mention fun colors that children adore), purchase a Junior heater for $9.99 (also at Walmart), and have a fish that will never need a tank upgrade that is still fairly hardy like a goldfish. For more info on bettas, check out the FAQ on the betta board.
I hope this has been helpful! Thanks for coming here to get more info on fishkeeping.