Generally, the prices for booking a mini-van on-line would be the same, or pretty close
to what you might find via phone call or on-site, (most companies will advertise that their lowest prices can be found online) but there can be variations, especially from local locations. Getting a low price on a minivan is rare, but research and time will help you find the best rate possible on what is normally a high demand, low supply type of vehicle.
In order to find the best deal on a minivan, I would suggest is to go to the company website and do some pricing research (make sure to check discount codes, if you qualify.
Also, make use of coupons that you may have, or check online for Free Rental Car Coupon Codes.
While it's rare to find coupons that apply to minivans, it can never hurt to check.
Find the cheapest possible rate you can, for the location, dates, times, vehicle, etc. and write it all down (or book it, if it does not require a credit card). Then call the location directly and do a price quote for the same thing. If you get the same price, you can tell them that you were able to find that price online, and that you were wondering if they had any "local" specials or "deals" , specifically for a minivan rental that would be better for you. Sometimes, the employee may be authorised to discount a rate even further for you.