Which one...
Your washer of choice depends on your needs and time. If you wash 5 loads in a conventional top-loader and it is in use all day long, don't get a front loader. High Efficiency washing machines usually have much longer cycles than conventional top-loading washers. I have a 30-year-old Maytag that can wash a load of laundry in about 30 minutes. My mother has a new GE front loader that will wash the same load in almost 2 hours.
For longest-life, find a used Maytag Dependable Care or even a used Maytag Commercial top loading washer. If in doubt as to whether it is the right kind of Maytag top-loader, tip the washer back and look at the bottom. If you see belts, it's the right one. Also, avoid any Maytag top loader that has a stainless steel wash tub.
Maytag Neptunes have mixed reviews. The Neptune top loaders can be lots of fun, but would likely be too unreliable for your needs. The more-common versions of the Neptune are front-loaders. Some of them have had issues with the control board and wax-motor failing, also the door boot. Before buying a Neptune, find out if these have been replaced. Also, a common problem with used front loaders of any make is bearing failure. If the machine's operators use normal detergent bearing failure is a great risk. To see if there is excessive bearing wear, run the machine on a spin cycle. If you hear a noise like a freight train roaring through the room, the bearings are shot and you should walk away from the deal because having them replaced can be very expensive.
If you get a front loader or a high efficiency top loader, be sure to use only low-sudsing detergent, most of which has an "HE" label. Although Fresh Start is usually fine even without the HE label. If you get a conventional top-loader you can use any detergent you like.
If you want to buy a new washing machine, I would recommend Speed Queen or Whirlpool. Whirlpool makes the same machines under many brand labels, such as: Whirlpool, Sears Kenmore, Roper, Best Buy Inglis, Maytag (the new ones with the center-dials) and Admiral (If I recall correctly). Avoid top-loaders like Frigidaire, low-end GE, Hotpoint, Maytag Legacy Series, Amana, and probably some more. Also, avoid any top-loader with a plastic tub. The guts of Whirlpool conventional top loading washing machines haven't changed much for over 20 years, and they are an excellent balance between cost and value. Get a new one or a used one, it doesn't matter much. Just watch the machine when it starts. If the load of laundry just twists left and right, the washer is overloaded, which results in a decreased lifespan of the washer, and doesn't clean laundry very well. The laundry in a properly loaded conventional top-loading washing machine will come to the top of the water at the outer edge of the tub, move across the tub toward the agitator, and then go down to the bottom.
The most common problem with Whirlpool's conventional top-loading washers is a broken drive coupler. This piece is easy and cheap to replace by yourself. It breaks usually after about 10 years of residential use, but its life can be dramatically shorter if the washer has been habitually overloaded.
I hope this helps,
Dave