Do not use a guitar amp for amplifying bass. The drivers are made to handle different frequencies, and its possible that you may blow a speaker or two or perhaps even the amp by putting bass through a guitar amp. You can, however, use a keyboard amp to amplify bass, and often get a very satisfactory sound. Best choice: Bass amp for bass.
I would like to preface what I am going to say by saying all of this is probably of little importance given the age of the player. You can go as cheap as possible and still get by very well at his level of playing. However, if you want something that will last a long time, then there are many different things to consider.
The realist is the best acoustic bass pickup I have heard to date. Its a little pricey at about $200, but its likely that your son can use this pickup through his entire career if it is treated with care. Other piezo-type pickups that I have heard are just not at all good.
I have never been able to get a good sound out of a fishman pickup and that is largely why I have steered clear of upright bass in the past few years. I have always had problems with feedback with the fishman pickup. also it gives me a nasty twangy clattery tone that I really dont like. This is not so with the realist. That thing sounds great and gives little if any feedback even when the player is right up against the amp.
Another option you may want to explore is getting a microphone to set up in front of the bass and get an XLR-1/4 jack adapter. This will give you many more feedback problems but will produce a good sound if done right. Combine a pickup and a mic and you have a pretty darn good combonation, but one that will likely be very spendy. The microphone way of doing things will be expensive if you want a good sound.
As far as amps go, brands to look for(listed in my level of preference):
Ampeg
David Eden (only placed below ampeg because of prohibitive price)
Hartke
SWR
carvin
Fender
All of these brands are a solid choice and sound really good (according to me)
I have a personal issue with peavey amps because I really dont like their sound. Many people do like the sound, but not me. However, they are usually widely available used and are built like tanks, which is probably a good choice for a younger player who may not be very careful with his equipment. DO NOT BUY A ROGUE AMP!! They are bad. Thats it. You will get little resale value off of an amp like that, plus they are crappy and I would not wish one even on my enemies.
Speaker size and configuration is largely personal preference, and since your son is not really old enough to have personal preferences yet, I wouldn't be too worried about the amp. They are expensive (no matter what the size) but can be sold off easily later on.
As far as power goes, depending on the size of the ensemble, I wouldn't go much below 100-150 watts. It is always better to have a little too much power than a little too little. Ideally, I think you may want to spring for a 2 ten cabinet with a smallish amp head. This is often more expensive than the combo amp route, but it will sound better, and offer more options later on for upgrading equipment. This is also a very solid choice if your son plans to play electric later on. (which he probably will want to do, given the state of jazz today, and the propensity of youngsters to become interested in rock and roll music) However, you can get by very nicely with a little 10-12 inch speaker in a combo amp if its got enough power. Just make sure that you get an amp with enough wattage to be heard in the band!!
Expect to pay $200-$300 (or more) for a useful new combo amp. You wont get much of anything with any power for cheaper if you go new. Used, you can find some great deals, you just have to be in the right place at the right time. Altogether, I would say you are looking at $400-$500, (this estimate may be a little high) depending on the setup, and remember the sky is the limit in this music business.
My advice to you is to go to your local music store (or one that actually has equipment to choose from if they don't) and poke around a bit. The internet is great for some stuff, but for trying out musical instruments, its terrible.

Check out
www.musiciansfriend.com, they are a huge company with lots of very cheap prices.
Well thats my advice.... lengthy, but I hope helpful. If you need more information, you can pm me or whatever, and I would be glad to help however I can.
Oh and if you get your kid a bigger amp, get him one with wheels or a cart to carry it on. Carrying such heavy items can lead to back problems that may plague him his whole life.