I usually recommend one of two routes, either adopt an adult dog or find a reputable breeder and get a puppy. I do a ton of rescue and foster work and my experience has been that so much of a dog's personality is pre-determined that you really want to know what the parents were like OR you want to adopt a dog that is an adult already and therefore more steady in it's temperament (can take until 2-3 for most dogs to show their fully developed personality/temperament).
If you want a puppy and are going to go through a breeder the MOST important thing you can do is to contact the breed club of that dog (usually easy to find by googling the breed name or can always be found on the akc.org website) to start with. They can usually put you in touch with your local chapter of the breed club or a local reputable breeder or owner.
Here is a little rundown of a good breeder...
They never breed a dog under 2yrs old
They show the dogs at a real dog show (akc or ukc) and the dogs are champions or well on the way (harder to get in some breeds than others, beagles are one of those breeds). Pretty much all the dogs in the pedigree should be at least champions as well.
They have very few litters each year, generally not more than one or two, with occasional exceptions
They do all testing recommended by breed club, usually this is at minimum checking hips or patella, having the eyes CERF certified each year, in cockers they would definitely require heart testing
They should be interviewing you as a potential owner as much as you are checking out them. I have yet to deal with a reputable breeder who did not have me fill out an extensive questionaire and insist on a phone interview at minimum, in one case I had to drive 5 hours to meet with the breeder to get on a waiting list prior to the bitch even being bred (and the bitch didn't even take on that breeding, *sigh*)
They should have a contract that you will be required to sign that includes having the dog spayed/castrated. They should also only be willing to sell you the dog with limited registration, which means you would not be able to breed it and register the puppies. Generally a breeder is only going to sell a show quality dog with full registration to someone who is interested in actually showing and not just as a family pet
The puppies should all be well socialized and raised in the home
The bitch should be available to meet, but not necessarily the male since making a good match between bloodlines often means going outside the dogs they own.
It should be in the contract that the puppy is never allowed to be given away or taken to a shelter/rescue and that if you cannot keep the puppy at any point in it's life that it must be returned to the breeder.
Okay, there's definitely more but that should get you on the right track of finding a reputable breeder.
As to which breed, I honestly am not a fan of cockers or beagles for families with children. I'd really recommend either finding an adult rescue, preferably one that is being fostered with a family or going to http://animal.discovery.com/breedselector/dogselector.do and looking through the suggestions. You might very well come up with another breed altogether that way, just make sure to look closely into whatever breed(s) catch your eye. Generally speaking most breed clubs website's will have an article detailing the downsides of the breed because the goal of the clubs is happy owner and happy dog, so they only want puppies going to people who know what they are getting into. Two of my dogs are rare/odd breeds but are absolutely exactly what I was looking for. In both cases I would never have stumbled across them by asking around (most people have never heard of them, lol) and it was seeing them listed on breed quiz sites over and over that got me to look more closely at them.
Whatever you choose to do I wish you the best of luck! It's a huge decision and I think by putting so much thought into it you are absolutely going to make the right choice.