Hi Quigg - welcome to gttalk.
Looking at the picture. You said you thought it was about 1962. I'm guessing 1963, but hopefully a Simplicity expert will shed more light.
I believe the bend in the gear shift lever and the higher steering wheel height suggests that it's a 1963.
(not that 1 year makes any difference - IMHO it's nice to be accurate if you decide to take it to a show)
As mentioned, one thing to look for is the play in the bevel gear box (BGB). there's a shaft from the motor that goes to the box. Lift up the front of the seat and the gear box is at the narrowest part of the body. Reach in the front of the BGB from behind the motor with one arm/hand, then "wiggle" the shaft that goes to the belt drive with the other. Really good is little to no play.
It has the hitch on the back. See if the seller has any implements.
I see the original badges is on the hood - which is great.
The briggs motor might not run without some "love". You man need to do spend some quality time with it to figure things out.
Before you try to start it, I recommend puling the air breather and carb. and make sure there isn't rust or any other contaminants that will destroy the engine. If you haven't rebuilt a flo-jet carb, there are some things you need to know. Come back and ask.
The first question you need to figure out is - why did they park it?
The starter/generator is gone. Could be something encouraging like it stopped charging. Pulled the generator, got a ridiculous price to fix it and decided it was time to replace the tractor. In the 80s it was an old tractor. 30 years later it's an antique.
That piece of iron and many precision inter-connected parts is a half-century old. It's been sitting for 30 years. It's going to take time to reverse the clock, but is worth the effort.
One last thing. To know more about that tractor (also known as a Simplicity 725), check out an extensive series of youtube videos from Zippo Varga. They are really, really useful. He covers a lot of topics.