You could make some pretty good vehicles for such a scenario, except getting fuel will always be a problem. There's always electric power but then you have to worry about a limited range and recharge times. So in reality most conventionally powered vehicles all have downsides.
If getting gas wasn't a problem however, I still wouldn't agree a go-kart as the wisest option. It's too low to the ground and offers no protection. You could maybe raise it, put big tires on it and build a cage/some sort of armour around it, then it might be pretty useful. I would want a fairly powerful engine, maybe 500+ cc's because you want to be able to run away; speed and agility is a big advantage but it's only so useful if it can only be used on roads.
I think I would prefer a bigger buggy, maybe with some armour and a good power to weight ratio. Using air cooled beetle parts might be the most practical solution here, since old VW stuff is pretty basic and still somewhat common. And it doesn't need an ecu, or coolant. It's possible to make them powerful and ideally, you could push 150-200 HP through a 2400 cc engine. With proper tires you could go almost anywhere at sufficient speed, and maybe with an extra large fuel tank, for a long time. Realistically though this might be a tough build without the resources to do it. But at least it would offer more protection than a bike or go kart...
