First off, $3,000 may well get you a nice used upright, but if you have your heart set on a digital, definitely check out all the contenders in that range: Yamaha, Roland and Kawai. In this price range, the Kawais have the most "authentic" action with their wooden keys (and the associated wobble...), and are generally nothing to sneeze at. The Yamaha's are typically the ones that everything else gets compared to, so definitely check them out (GuitarCenter usually has plenty of models to play around with). As it turns out, you may not have to spend more than about $2,000 to get a very good digital (say, the Yamaha PF-500; the Kawai's cost a bit more). For the next step up in terms of "authenticity" (it's all about the action, the sound samples are generally very good in all models), you'll have to spend a lot more. Spend the remaining $1,000 on a teacher and material instead.
Whatever you do, take ample amount of time to play on all the different models in your price range. If necessary, take a teacher or a friend who can help, and of course, take your son and see what he likes best.
Finally, there must be about 1000 threads on this particular topic. Check them out for more info.
Good luck!