When I start the truck, I hear a ticking noise for about a minute until it warms up. Then it makes noise when I step on the gas pedal.
The noise you hear when first starting is the oil pressure building up, and the hydraulic cam followers getting pressurized. Once they get oil pressure, then the noise goes away. Try using only the Ford FL820S oil filter, and only oil specified for your truck. Most are 5w20w, but make sure you confirm by checking the oil cap. The other noise you hear while accelerating is the cam phasers, most likely; you will need to have them checked to see if they should be replaced. I recommend having a mechanic, such as one from YourMechanic, inspect the source of the noise in order to properly diagnose the issue, and quote the repairs needed.