["You" = "original poster"]
I'd be inclined to run it up before changing the coolant and radiator and heater hoses so as to dislodge any rust. This as part of a general program of changing all the underhood and undercar hoses and fluids. Watch those brakes like a hawk afterwards -- actually, consider rebuilding the rubber hoses and wheel cylinders on general principles. They have a hard life down there.
You might want to drop the pan and change the transmission screen and gasket too, if it's an automatic (sounds that way from the description).
As for rust in the fuel tank, you might be able to get away with changing the fuel filter repeatedly*. You didn't say what year or engine, but I'm imagining the "jelly jar" arrangement where a metal filter housing screwed into the bottom of a mechanical fuel pump. Very handy to take this approach with those, especially if you just happen to be changing the oil filter (access is easier with the oil filter off), as they have a lot of capacity and the larger particles drift to the bottom where they're easy to admire and swab out.
My old T-bird with a 390 horked up a fair bit of rust and fines at first, but after doing this every few months on a boring afternoon for a year or so, I wasn't finding much anymore. Funneled the gasoline into my lawnmower through a coffee filter, screwed the thing back in with a new filter cartridge, lather-rinse-repeat.
Watch very carefully for gas leaks (incl. on and near the carb itself) during those first few run-ups, and, well, for leaks of everything else too.
Definitely change out the differential fluid. The cheap pumps that are powered by a drill are great for that sort of thing. The oil is too heavy for a hand vacuum pump like you might use to bleed the brakes, and of course it smells like Hell in a pretty literal sense.
--J