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«primarily for hospital patients with painful conditions»

Assuming they are going to recover.

Turtles. Very sturdy, easy and cheap to keep, long-lived. You can also reduce their metabolism and keep them lethargic.

Otherwise, dogs. Not so cheap, and require way more space. At the same time, they're more active and could supply more enjoyable experiences.

In the long run, probably the law would start including sentences to "temporary obliteration" (i.e. involuntary hosting) for those crimes where rehabilitation is either unlikely or pointless. In those cases, criminals would be sentenced to a certain period of time during which their bodies would be occupied by someone else. Since the new occupant is a productive member of society, and the criminal is, to all intents and purposes, nowhere, less prisons are needed. So, another possibility becomes «humans».

This opens other interesting problems though: what if the new occupant damages the body? Or even modifies it - "Hey, I got two years for embezzlement, I expected to find myself aged two years, not tattooed over!". What if the new body enters a relationship? Involuntary hosts probably will require some visual identification, unless they're confined to the hospital or dedicated towns.

As much as there might be a trade in recreationally adopting the form of a golden eagle or a porpoise. A very safe and efishent storage vessle would be the goldfish:

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Lifespan 5-10 years, small and easy to feed and house, cheap to replace when obsolete.

In a cash-strapped society this would be suitable for low value citizens, welfare-state cases or prisoners.

African Grey Parrot.

When the economy permits.:

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With a 40 to 60 year lifespan and the ability to communicate in recognisable human speach (not to mention fly) this would be a great option.

The better off citizens would I'm sure be given the choice of their preferred animal from among a suite available at each medical facility.

Ultimatley, the law of supply and demand will allow people to become whatever they want. There might be some illegal options such as an adult mayfly (too short a lifespan) or a planarians (people would be able to infinitely clone themselves and their memories at will) but commerce will prevail, it always does.

Commercial concerns.

Where commerce is concerned, fads and fashions will I'm sure come and go, the fallback option in times of financial chrisis will be the expedient and cheapest - the old goldfish.

Addendum:

Hospital administrators could find that there developes an illicit trade in revenge-consciousness transfers - "Do you know someone you'd like to see as a cockroach dancing on a hot tin-lid? We have the answer."

Society would then, of course need to cope with the illicit trade in body upgrades and people turning up at police stations claiming to be someone else. Interesting issues your world throws up.

Pigs.

The pig anatomy is very close to our own. Even the pig nervous system and brain structures are very close to human. Pigs even have a similar social structure.

So it would be a short acclimatization period for the human 'mind' to adjust to the new surroundings and body.

The biggest relearning curve would be walking on four legs vs two.

The drawback is the shorter life span of the pig - 15 to 20 years potential.

Mantis Shrimp, for the wealthy

Although the idea of being a shrimp seems weird, the experience will surely be worthwhile, and should keep them entertained for the duration of their habitation.

Being a Mantis Shrimp would be cool for a couple reasons:

• The claws of certain species can accelerate to 83 km/h, and hit with an impact of 1500 N. This is so fast and powerful even the shock waves can kill prey, and the claw itself can destroy aquarium glass in some species.


• They have the most advanced natural visual system that we know of, anywhere. Some species of 16 different color preceptors, meaning that you would need to mix 16 primary colors to simulate colors accurately for them. From their point of view, we have a severe decatotritotan form of color blindness. This means that they perceive qualitatively more colors than humans. Their vision also extends into infrared and ultraviolet. They also see all qualities of polarization, whereas we see none (except linear polarization very slightly). Finally, their eyes can point in any two directions, and each have individual depth perception.


• To go along with the last point, their bodies can produce color willfully, being able to produce nearly any color they can see. 16 dimensional color vision and color production would surely be a boon for artists!

So, I think being a mantis shrimp would be rather fun.

How has no one said ape or chimpanzee yet? They're the animals already most similar to humans.

There isn't one answer, because you are applying the idea to different situations.

Prisoners

Used as punishment, you want something that's easy to handle, not dangerous and having big troubles running away. So something small, harmless and slow is best. Snails are out (not vertebrates), but there are also really small frogs, or of course, fish. Fish are generally easy to keep and can't run away due to lack of legs. Aquarium, done. You want to pick a species with a life expectancy higher than the prison sentence, or change bodies every few years.

Hospitals

Completely different requirements. You need something that is comfortable for the patient for a limited time. My best idea is cats. They sleep a lot (about 16 hours a day) but when they're awake, from what I see they are having fun, they are quite sturdy for their size and can reach places and do things that neither humans nor most other animals can. However, that would only be your default offer, because patients would most likely want a choice. Many people will want to fly, so you'll probably have some birds on offer as well as flying lessons.

Tardigrade

While you said “Any vertebrate is capable of holding one human mind for an unlimited amount of time”, you did not specify if non-vertebrate is capable of hosting human mind. If the mind transfer process applies to all animals, and if size doesn't matter, I'd suggest Tardigrade as a good choice.

Tardigrade is known to have cyptobiosis, namely they can suspend their metabolism. They can survive under extreme environments that would kill almost any other animal.

(mostly from wiki)

• Low temperature: few to days at 73K, few minutes at 1K.


• High temperature: few minutes at 151°C.


• Extreme pressure: vaccum of open space and solar radiation combined for at least 10 days, or more than 1200 Atm.


• Dehydration: survive 10 years of dry state.


• Radiation: Tardigrades can withstand 1,000 times more radiation than other animals.

While their average life span is only a few month, they can be dehydrated to skip a rather long time period; and the fact that they are "immune" to most fatal factors for other animals, I find it suitable for a 'storage' for human mind, especially for those who just want to stay safe and wait until their operations end.