I sugest you keep the saw and check YouTube for how to tune up a table saw. There are numberous strings on the site about how to remove rust. Do a quick search and you'll find them.
I would even be reluctant to replace the motor unless it wasn't able to work without stalling.
The essence of the table saw is precision, and that comes from the alignment of the blade with, first, the miter slots, then with the fence. The fence would be the thing I'd spend my money on. Several suggested above are quite good. You might consider getting one small item, a Wixey angle guage, about $31 on Amazon.
https://www.amazon.com/Wixey-WR300-...=1494106300&sr=8-1&keywords=wixey+angle+gauge This will allow you to set your blade to exact angles fairly easily. Half a degree off will make it impossible to get a good glue up. This needs to be done frequently, impacted sawdust can mess up the angle over time, so can vibration.
There are no safety devices on older saws, so you should get at least one Grripper, a special push block designed to keep you hands and the blade safely far apart. This also allows you to push down, forward and against the fence all at once.
https://www.amazon.com/dp/B001I9UNW...=grr-ipper&pd_rd_r=WJ2X48SF9AZH8FAAMQF0&psc=1
Develop some habits, such as standing to the right of the line of the blade so if you get a kickback (fence alignment in, instead of slightly out, or trying to cut warped wood). This is when the back of the blade catches the wood and shoves it back at you at speeds of around 100 mph. Big ouch, big bruise, long time sore spot, possibly a bruised or even cracked rib.
I NEVER push anything toward the blade with a hand or digit in line with the blade. I have a habit of keeping my thumbs IN when using any saw and simply cannot place my hand withing 5-6 inches of a spinning blade without a push block. Use a push block or stick or the Grripper at all times, Of course, no drinking before or during tool time.
Align the fence so that it is maybe 3 or 4 thousanths out from the blade path at the far end. This is trivial for alignment, but pretty much ends kickback. You do this by aligning the fence to the miter slot, which is why you want to make sure the blade is aligned with the miter slot. I count this triple alignment as so important I have a Woodpecker gadget for the purpose (probably overkill).
As you go along, you'll most likely want to build a table saw sled so your crosscuts are dead on 90 degrees. I also have a Rockler sled that allows cutting angles with ease. Worth it to me.
When ripping a thin piece off a wide piece, keep the wide piece against the fence and the cutoff will simply fall off. Putting the thin piece against the fence is called trapping, and it is the recipe for kickbacks.
The miter gauge is another thing. You probably still have your dad's, and it is probably still good. But all of these need to be aligned. Nothing does that better than a good draftman's triangle with precise 90 and 45 degree angles. Rockler makes a good near quarter inch thick one that's big enough so you can position it on the blade (not touching the tips), then push the gauge up to it and adjust until the gauge is dead flat against the triangle. You can't trust the markings on most gauges, and all gauges can be wrong it the blade/miter slot alignment is off.
Sawdust will ruin your lungs! You have to wear a good quality mask. 3M makes some disposables with a small valve that lets air out, but not in. I have a battery operated vented mask that has a small fan drawing air in through a filter. This gives a positive pressure in the mask so sawdust is always being blown away. It doesn't interfere with my safety glasses, in fact on mine the air leaks out just under my glasses so the don't fog up. In some climates, this is a real bonus. Rockler has this on sale now for $60. Get a couple of sets of AA rechargables for it.
Power Air Respirator | Rockler Woodworking and Hardware
You've gotten many helpful suggestions about renewing your saw, but I wanted to make sure you got some safety info. as well. Lots of people get careless or cavalier and lose digits every year. Have fun with your fine saw, but be careful.
And I'd like to know your first name as well.