Full size vans work. They are less expensive used than pickups, particularly passenger vans coming off short leases or out of the rental fleet. Early 2014 I found a 2013 E-350 12 passenger with 19,000 miles for $21,000. E-350 extended (15 passenger) were selling about $1000 higher. Chevy Expess 3500 12 and 15 passenger running about $800 more tha equivalent Ford.
Regular length "1-ton" passenger vans usually have capacity to carry 3000 pounds passenger and/or cargo, depending on the GVWR (assorted ratings optional for tax purposes), extended vans about 300 pounds less.
Express 3500 passenger van ex-rental will usually have the 6.0 V-8 with a towing capacity of 10,000 pounds when empty, about 7000 fully loaded. E-350 passenger ex-rental will have the 5.4 V-8 with 13,000 GCWR for 6500-6700 towing capacity empty, about 3500 fully loaded. These vans hardly ever get fully loaded, that would be 12 250 pound passengers in the regular van, 15 200 pound passengers in the extended.
Cargo vans will be cheaper new, and have about 800 pound more carrying capacity or tow capacity foe same ratings, because that's about what the seats, trim, rear air conditioning and other passenger comforts add to the empty weight of the van. Cargo vans also often get bought with smaller engines, which can reduce towing capacity. They are harder to find low mileage used because commercial leases are more like 3-5 years and customers who buy the vans run them until fully depreciated or they wear out, which can be 200,000 to 300,000 miles or more. (That also happens to passenger vans bought for hotel shuttle or taxi service, running sometimes to 500,000 miles).
I suggest passenger van because carrying dogs, you want the big airconditioner cooling the rear of the van, and the insulation, heat and sound, of the interior trim. You can pull out as many seats as you want for the right mix of cargo and passenger capacity. I pulled the 4th row seat from my regular length 12-passenger, so seating for eight and about 120 cu ft cargo space. I can pull another row to have seating for five and about 180 cu ft.
But why not a truck. One of my RVing buddies raised bird dogs for competition and show, always carried his kennels in the back of a pickup, but these dogs are also kenneled outdoors year round. Maybe if your dogs live indoors, you might want to carry them climate-controlled.
Tom Test
Itasca Spirit 29B