Ok, so I have a '96 c2500 5.7 350. I recently had new tires put on, cheap one's at a used tire shop a while back before winter, and I am questioning the tire pressure in my tires. To make the matter slightly more complicated, the size of my original tires was: 245 / 75r16 but the tire shop didnt have that size, so I went with: 265 / 75r16.

So, all 4 tires are:
265 / 75r16.

The stiker on my door says to inflate the tires to:
front: 45 psi
back: 80 psi

Would I still use these #'s for my tires (keeping in mind the larger size) or would I instead look up the manufacturer's suggestions for each tire (keeping in mind all tires are different manufacturer)?

 

You would fill them as stated on the tire.The numbers on the door are recommended for the tires that were supplied with the truck when new.Now if you went with the exact same size tires as was on the truck when new you could follow the pressures on the door.

 

The tire will only list the max inflation pressure of the tire.

You can use the placard setting on the door if you have the proper load range of tire. Most 2500 series trucks require a load range e.

What is the load range of your tires?

Not sure about your year but 2000's and newer can have the speedo calibration adjusted to match the tire type and size. It is done with the factory scan tool through the ebcm.