Finally saw my name on this... :
Choice of Poop:
Like others have said, horse (or donkey or other one-stomached hay-and-stick-eaters) will have longer fibers.
Cow and other ruminants, shorter fibers. Cow dung is very commonly used in Africa, however my experience has always been that it breaks down into sawdust-like micro fiber, not much holding strength for the crack-resistant base coat that I'm usually looking for on an exterior plaster.
I have not tried buffalo. I would imagine they're like a souped-up cow (because you can cross-breed them, and I have never heard of cross-breeding averaging out the number of stomachs between differently-endowed species....)
However, if they are eating a coarser diet, with bunch grasses and woody material, you might get more interesting fiber results.
Fresh dung, screened and/or soaked for a day or two, does seem to work best. I don't love picking out baby bugs (aka maggots) from older dung.
I have not tried dung from camelids including alpaca. They do chew cud so presumably, multiple stomachs and smaller fibers.
However, they have the interesting habit of always pooping in one or two piles in a pasture, making it easier to harvest than most other pastured herdbeests.
Testing:
My biggest suggestion would be to do some test samples, try the different dungs and different proportions of fiber:clay. You can do entirely without sand if you want, but keep in mind you need a LOT more aggregate (sand or fiber) compared with the actual clay content. If your clay is too sticky, or you use too much, it will crack. Thus letting weather and bugs in, while probably not letting trapped water out fast enough to compensate.
I'd use quart tubs for proportions, mix about a bucket each of several options, and give it a test. Both on your wall, and on a smaller sample you can mess around with (bake in the oven, etc).
Try: (fiber/aggregate to clay)
1:1
2:1
4:1
6:1
8:1
It can be hard to get your clay to a really consistent, creamy texture so that your finish batches match your test batches. Start processing the clay early, let it soak a long time, and pay attention to how it feels as well as the proportions in each test batch. You may have to 'doctor' the subsequent batches (add a little more clay, fiber, or water) to get back to the consistency of the original.
There is nothing wrong with mixing fibers, but I would be hesitant to make my recipe more complicated than necessary.
It would be OK to mix in a second type of fiber if you run short on your main one, or switch types from coarser to finer for the finish coat.
Hair?
If you have access to all these types of dung, you might have access to another fiber that some of us can't easily get.
Animal hair (typically horse or goat, hair rather than wool) was the traditional fiber of choice for hard-wearing plasters, and can be stronger for its weight than cellulose (dung, grass, or paper fibers). It may not be easy (pr pleasant) to get it from the hide-tanner processors in any condition you'd want to touch, but some people have good results looking up animal groomers, sweepings from pre-show grooming at local fairs, or other cottage-scale sources.
Health & Hygeine
I do tend to wear gloves when getting my hands into plasters, even if they're the mesh-backed garden gloves. It's easy to sand off your fingerprints, or jab yourself on rusty tools or bits of wire that stick out of a bale, and then you have an open wound near potential disease vectors. However, if you are good with your plastering tools, you may be able to do the whole process without actually touching the plaster (common practice with lime-based plasters, whose alkaline ingredients are not good for skin).
I recently had a chance to ask about disease vectors while plastering with a naturopath who also studied veterinary medicine. My impression has always been that horses share slightly fewer disease with people than other farm animals. She didn't disagree.
In her project, she did go for a horse dung, supplied by friends who regularly worm their horses (using some of the more responsible/less toxic worming medicine), to avoid equine tapeworm.
She confirmed that from a disease-control standpoint, the diseases you can catch from horses may not be as numerous or severe as from some other animals.
With sheep or cattle, there are some more lasting nasties that could be transmissible.
From the CDC website's page on farm animals:
https://www.cdc.gov/healthypets/pets/farm-animals.html
Most livestock dung could contain e. coli, salmonella, and other bacteria or viruses such as cryptosporidium (most common in younger calves with diarrhoea).
Sheep, goats, and cattle are slightly more likely to carry anthrax, brucellosis, and a few other diseases.
Pigs would be significantly worse - they share more, and more serious, diseases with humans. But as they don't generally eat enough hay or woody matter to produce useful fibers, we avoid pig dung (and other omnivores' dung) anyway.
Some of the worst diseases that can be carried by farm animals would not likely be transmitted through dung, instead they are transmitted by mosquitos, or by eating raw milk / young cheeses.
So the biggest thing, whether or not you wear gloves, is: WASH YOUR HANDS BEFORE YOU EAT.
WITH SOAP. and clean water.
I like to use a big outdoor bucket for roughly rinsing hands and tools (keeps sand and clay from invading the plumbing).
Then wash again with cleaner water at a hose-tap near the house.
Anyone handling ready-to-eat food for other folks would be wise to wash again in the kitchen, just in case someone has contaminated the doorknobs or whatever.
I tend to keep tools in one area, and give all tools including the handles a good rinse at the end of the day.
And in case it's not obvious, I don't like to mix food processing gear with plastering/dirt-sifting gear.
If I need a fine sifter for finish plasters I will make a new one from window screen, not use a kitchen sieve or dehydrator tray.