New Lift! Gear oil?

Hello Gents, I just got a 4-post lift in my "compound" and so far it is awesome. I bought it gently-used off FB Marketplace for $1800, and did the install myself with the help of my lovely wife. Now that I'm under the car, I'm cleaning underneath, marveling at how clean the car is for an Ohio car, (only light surface rust underneath) and thinking about changing out the differential oil.

So, any recommendations on changing the gear oil? Should I suck out the old stuff, or simply top...

New Lift! Gear oil?
Author: Richard Reau