Of course Sears records go back that far. If someone there told you that, they just didn't want to bother checking. SearsPartsDirect has machines from the '60s, at least as far as parts diagrams, etc.
If your machine is a top loading automatic, and by the model number it looks like it is, there were only two basket capacities then - 2.5 cu ft. and 3.0 cu ft. However, due to a couple variations in the Dual Action agitators that were available in various models, capacity has varied on the larger tub to a recent high of 4.0 cu ft. in the same porcelain on steel wash basket.
All you really need to do is determine if your machine was rated as an Extra-large or a Super capacity, then shop accordingly.
If you want something somewhat similar, I would put my money on another Whirlpool built machine just like what you have. Kenmore, Whirlpool, Estate, Roper, Amana, Maytag, Inglis, or Admiral are all basically the same. You should be able to look at the basket size and see if what you are looking at is similar. Don't let a salesman give you some bull about front loaders, unless that's really what you want. This should not be overly complicated.
Why are you replacing this machine? Is the current machine broken? There are some common very easy fixes that can be done to keep your machine running, as a 1996 machine, unles you've used the heck out of it, may not necessarily be "done" yet.
Gordon