Also check the radiator for the correct chemical thingy I cant remember right now a cca level maybe? I am sure diamond pilot knows what i trying to say......
FYI I owned a 2000 f250 just like that is was the best tow vehicle of all three diesels I have owned 2000 7.3psd 2003 6.0psd 2007 6.6duramax
SCA is needed in the Antifreeze coolant for a 7.3. Can get it as a separate additive, or some HD diesel older generation (green type often) antifreeze is available pre-charged with SCA. Not sure if this is your first diesel - on this type of engine, SCA is needed in the coolant to prevent cavitation corrosion in the block.
Use a good quality
diesel motor oil. It is also used to control the fuel injectors on the 7.3. Needs around 15 quarts, give or take. I usually run Rotella - most any Mobil 1, Delo400 etc should do you fine.
Your pickup might have a Transmission temperature gauge stock. My van with a 7.3 didn't, so I bought a Scan Gauge II - it sucks data out of the OBDII port. I have 2 of the 4 displays on my Scan Gauge II programmed to display Engine Oil Temperature, and Transmission Fluid Temperature.
Warmer down your way, but up here, a 7.3 takes quite a while to bring the Transmission fluid up to operating temperature. The 4R100 automatic trani is the weak link - like any automatic, lifespan can be shortened by skipped fluid/filter maintenance, or hard use. Unless you can trust that it has been serviced recently, put the ATF and Diffs on your Fluid to Change list.
Of that era, the 7.3 and Cummins 5.9 are some of the best regarded diesels. You definitely scored a great buy, congratulations.
Rgds, D.