I wouldn't put a dump insert on any truck under a 4500, especially if you plan to tow the chipper behind it, the insert will be 650-1000 pounds on its own, you want at-least 10 yards, so there's 5000-6000 pounds in chips alone, so lets say 7000 pounds in the bed of the truck + 6-7000 for the chipper (assuming 12" chipper like most of us run)
a 3500 with airbags would probably handle it but you will be well past your rear axle weight rating
your best bet is going to be a single axle dump truck and make a plywood box, the older international's are good trucks but a little expensive, ive got a GMC Topkick but parts are near impossible to find for them and not cheap when you do find them
occasionally theres a 15-20yd chip truck for sale on FB Marketplace for under 10 grand, I personally would look at an F750 with a box, or a retired asplundh bucket truck and take the boom off, put a mini skid platform where the turret mounts, unless you can keep up on inspections and repairs the boom is a waste of time and money if you wont use it daily
no matter what you get, make sure the box is a PTO dump and not electric, the PTO is more expensive but will last a long, long time, plus you can run aux hydraulics for something like a polesaw, the electric ones overheat fairly quickly when dumping heavy loads (chips arent heavy, but you will eventually put logs in there)