Motor mounts replacement

Welcome to 2CarPros. Motor mounts don't usually rattle, they will transmit vibration from the engine and with the hood open you can put the truck in gear and step on the brake and and the engine will move around a lot when you step on the gas.
Rattles over bumps are commonly the sway bar end links or the sway bar bushings themselves. The easy way to check those is to disconnect them on each side and then see if the rattle is gone.
For the shocks the rears are easy. Jack up the truck, remove the rear tires and you will see the shock retainer bolt on the bottom and the nut that holds the top in place on the top of the frame mount. If it has the active ride units there is also a banjo bolt that holds the line in place.
The fronts are more work as they are coil over units. If you have the non-adjustable air suspension you can get units that include new springs and upper mounts that are much easier to replace as those are simple bolt in parts. If it has the air adjustable option it gets more complicated as those are a dealer only part that run almost $300.00 each and would require you to dismantle the mount and spring from the strut so those parts are reused.

Do you have the air suspension option?