A service dog and an emotional support animal (ESA) are two very different things.
A service dog is trained to abide by public access standards when it accompanies its handler in public. It performs tasks that help mitigate its owner's disability.
An emotional support animal is more of a dog that provides comfort, and doesn't generally do any trained task for disabilities.
While there is no size limit on an SD, a tiny pup will be limited in certain things. People are also very judgmental because they think if there's nothing physically wrong with you, you just have a 'SD' to you 'can take your dog anywhere'. Not to mention, you need to make sure your dog doesn't get stepped on. What size dog you need depends on the tasks you want the dog to perform. But there ARE service dogs for people with maybe not 'physical' limitations, such as a wheelchair, but autism for example.
Please Don't Pet Me - a good link
ESA handlers do not have public access with their ESAs EXCEPT for housing and airlines due to the Fair Housing Act and the Air Carrier Access Act. So you can live in no-pets housing with them and you can fly with them. I just learned that some states/towns do have public access laws for ESA handlers and parts of California allow ESAs anywhere a service dog is allowed.
Most people who get service dogs and train them themselves are VERY specific in what type of dog they get. They search for the RIGHT breeder and the dog that has that right temperament. You also have to realize that you may get a dog, train it for 2-3yrs, and then it's NOT the right candidate, and be able to access that. It's a hard decision to make when it's your pet dog as well who you have bonded with so most just keep washed out service dogs as pets.
Also SD's don't just need regular basic puppy classes. They need classes specifically for service dogs. They need 1000 times more socialization, more positive experiences, etc... if your pet is spooked by... someone in costume, for example, it's really not a big deal. More of an annoyance. BUT, a service dog that is spooked by something like a shiny floor... that will be a big problem. Finding a GREAT trainer that KNOWS what they are doing is important too. Not your run of the mill petsmart trainer.
Buy just 'buying' a certification online is not good at all. And all will be doing is harming those who truly need SDs to get by in life.