Which Dog Breed Is Right For Me?

Those dogs you mentioned are mutts, they are not breeds.
For what you will pay for a mutt why not buy a pure bred dog.

Well none of the dogs you mentioned here except the lab is a breed they are all designer mongrels not breeds of dog at all therefore.

You are NOT planning to ADOPT. Stop using the INCORRECT term. If you are looking at "Poos" or "oodles" then you are going to BUY from a BYB. (Shelters are NOT full of poos or poodle mixes, so choice would be very DIFFICULT & not the "wide-open options" you are indicating.) Shelters are full of: pits, pit bull mixes & Chihuahua.

If you really want a dog that doesn't shed, then buy a dog that is a BREED that doesn't shed and has KNOWN characteristics that meet your needs. Poodles mixes are extremely variable and if crossed with a SHEDDING breed, you have a 50/50 chance of getting the SHEDDING genes.
Here are two links you need to read, before deciding on a "poo" or poodle MIX:
http://www.canismajor.com/dog/poodogs.html

https://www.psychologytoday.com/blog/canine-corner/201404/designer-dog-maker-regrets-his-creation

Here are non or low shedding breeds;
http://www.dogbiz.com/faq-allergies.htm

Why on earth would you consider paying any money for a mongrel from a back yard breeder, the worst scum on the earth next to a slumlord?

Buy a purebred from a reputable, professional breeder or look in Petfinders for an attractive adoptable pet. If you want to train a service dog, get a real trainer and do it properly. It's more difficult than it should be for the public to accept genuine service animals when so many people try to pass off their house pets as trained when they are nothing but "Mommy's furbaby."

Poodles and Havanese are nice dogs. Poodles are very smart and don't shed(much at all). Bichons are notoriously difficult to housebreak.

The one you have the finances, time, fits into your lifestyle and can provide basic care; http://i40.photobucket.com/albums/e224/GLLNTKNIGHT/dogcare_zpse256a844.jpg

None of the ones you mentioned are breeds, they're mixes.

All dogs shed, some more than others.

And what Service will this mongrel be performing to mitigate a physical impairment (or severe psychiatric impairment) that substantially limits your ability to perform at least one major life activity* without assistance?.

*These consist of functions such as caring for yourself, (including bathing, dressing, shaving, preparing a meal, and going to the restroom), performing manual tasks, eating, sleeping, standing, walking, lifting, reaching, bending, seeing, hearing, speaking, breathing, learning, reading, concentrating, thinking, communicating, interacting with others, and working.

Adopt? These are all backyard breeder mutt mixes that you'll only find by paying a **** load of money to some lowly backyard breeder. Why on earth would you support the breeding of mutts for money?

Your dog also is NOT going to be a service animal. Service animals are professional trained to assist the blind, the deaf, detect seizures, etc. What you're talking about is just yet another bogus "Emotional Support Animal" and there's no training, licensing, registering, insuring as it is JUST A PET.

I would say a miniature goldendoodle. It is a small golden retriever-poodle mix. My friend owns one who is three years old, and she is absolutely adorable. She knows many tricks and has been taken to obedience classes. She is very respectful, and does not shed whatsoever. We have an airedale, but they grow to be fairly large, even though they do not shed. Hopefully you find the right one!