Three possibilities come to mind.

1. Worn belt(s). The machine has two belts. One runs from the motor to the transmission, the other from motor to pump. ONLY specific Maytag-brand belts must be used, as the transmission belt functions as the machine's clutch, designed to slip during spin (not during agitate) until the basket gets up to speed. The two belts must be replaced as a pair. Easily replaced from beneath the machine, simply tip it back, slip the old belts off, new belts on. Sounds like this may not be the problem since you say spin is OK.

2. Worn or sticking motor carriage. As part of the belt-clutch design, the motor is mounted (at the left-front corner) on a spring-carriage assembly to control belt tension. If the springs are fatigued or the carriage rollers are worn or sticky from aged grease, it won't adjust itself for proper tension. A repair kit is available. The motor and carriage are accessible by removing the machine's front panel -- two screws at the lower front, then the panel lifts up/outward and unclips from the top.

3. If the machine is VERY old, the transmission oil could be thickened with age. Operation in very cold environ such an unheated basement or porch will make the sluggishness worse. This is a more major repair, but if the machine is otherwise in good condition, you may consider doing it, and the tub bearing checked and replaced if needed. These classic Maytags will run for YEARS more after a refurbishment.

4. The spin squeak may indicate the felt damper pads that cushion the support base are worn (a repair kit is available). Once they wear down completely, metal-on-metal results when the tub oscillates during spin, VERY noisy. Or 1) the brake is badly worn, needing replacement; 2) the brake needs lubing (Maytags have an "oily" brake design).

The folks at www.automaticwasher.org should be able to assist you in solving your problem.

Thank you both. I'll report back later what is found, but don't get in any kind of a hurry about much so long as something is at least operable. Yesterday I did a load of jeans, paying attention to the quantity of them, and the load size, and the agitation seemed OK though not the greatest.

Here is a pic of a washer that looks exactly like mine. I can't read the metal model tag on mine though.

These classic Maytags will run for YEARS more after a refurbishment.
I don't think appliances today are made to hold up and last like the older ones. After reading of so many problems folks have with new, or near new models, I figure I am a lot better off keeping what I have and repairing it, even if I have to hire it done, if it doesn't end up costing a lot more than it is worth.

btw...I paid $75 for this washer about 5 years ago, when my 20 year Kenmore gave out. I've already gotten my moneys worth out of it. I needed one right away, and didn't want to make a snap decision on what to buy new.

Sue

Well figure 75 dollars a year for 15 years just to purchase a new one of comparable quality, and then figure about 50.00 more for repairs over the same years at least. If you are lucky enough to get that many years from it. Odds say you will be lucky to get 10 from one today.