For unmanned vehicles, I don't think the radiation belts pose any significant threat. Any deep space probe bound for Jupiter would already be radiation hardened. The radiation levels around Jupiter are much more intense than our belts. While not certain, it wouldn't surprise me if Saturn and the other gas giants have substancial radiation belts of their own.

A NERVA style solid core reactor can produce high thrust levels but only for a short time. If memory serves, NERVA was only designed to produce thrust for about an hour. A nuclear-electric approach can't generate high thrust, but can can produce constant thrust for months, perhaps even years. That would result in a far higher velocity than a NERVA style engine. The nuclear reactor could also provide electricity and heat needed for the entire mission profile.

I think the VASIMR concept has a lot of promise. The idea of higher thrust when necessary combined with higher Isp for the cruising phase gives a lot of flexibility in mission planning.