You don't need anything special to run a trackday, though a sprinter van is going to be excluded from anything but parade laps. I've run my stock 2004 Accord winter beater at several trackdays, and even loaned it to a friend for a few trackdays. Just tossed a set of pads on the front, all season tyres and all. A week and half ago I ran my also stock 1999 Civic, which if you don't get seasick from the body roll is still a pretty fun car lol.
You can drive the sprinter on track for paced laps at Track Night in America, but they don't run at RA, I think Blackhawk Farms would be the closest. Their paced track tour laps are free, and because they are run at highway speeds you do not need any safety equipment, not even a helmet.
There are shops that rent cars for trackday use, though they are usually going to be race cars rather than street cars. A spec miata runs about $800 per day for hpde use in the Northea$t. Not cheap, but I generally wouldn't recommend anyone rent a race car for an hpde anyway. For a number of reasons.
