The different regional local AAA clubs are run semi-independently, each with their own quirks. For that reason, no one can give you (good) advice about which membership level to choose from, since no one knows exactly what Basic vs Plus entails for your particular club. Some clubs don't even have more than one level of membership.
For my local club (AAA Hudson Valley, in New York), the differences are:
Basic
Plus
Towing Mileage 3 miles 100 miles Fuel Provision Pay Pump Price No Charge Lock Out Service up to $50 covered up to $100 covered Trip Interruption N/A up to $350 Passport Photos "discounted rate" free
Going through those one at a time:
* Towing mileage - this is the number of miles AAA will tow your car if it breaks down, free of charge. After this limit, you'll get a bill in the mail. I don't know offhand what the rate per mile past this limit is, unfortunately. I've never needed it. Everywhere I've broken down, there's always been a repair shop within 3 miles.
* Fuel Provision - people who need this are just silly. If you manage to run out of gas, they'll come to your car and give you a couple gallons to get you going again. A basic membership charges the average price at your local pumps. A plus membership doesn't charge for this service. Seriously, though, running out of gas? How often does that happen? And if it does happen to you on a regular basis, AAA is the least of your particular problems... ;-)
* Lock Out Service - if you lock yourself out of your car, they'll call a lock smith and pay for up to $50 or $100 parts and labor for the lock smith's services. After that, you pay the remainder.
* Trip Interruption - if you book a trip through them, and your trip is delayed for more than a day due to automobile problems, a Plus membership will reimburse up to $350 of your lodging, meals, or alternate transportation.
* Passport photos - Plus members don't pay, basic members do.
I personally don't think any of this is worth the additional cost of a Plus membership. Annoyingly, my local aaa site doesn't give the price for a Plus membership online, so I can't give you an example of the price difference. A basic membership is $46/year plus a $10 one-time enrollment fee.
I will say that AAA is one of the best investments I've ever made, and I can't imagine not having it. In addition to the road side assistance (which I've used for everything from a dead battery to a flat tire (with no spare)), they provide maps, trip-ticks, and guidebooks for pretty much anywhere in the country, free of charge. Showing my AAA card at random businesses has gotten me everything from 10% off oil changes, to 15% of eye glasses, to a free dozen Krispy Kreme donuts. They also have discount tickets to places like Six Flags and Walt Disney World, not to mention local movie theatres. You should definitely get AAA, for both yourself and your son. I'm just not convinced there's sufficient need to upgrade to Plus.