So you know what you want! That's a great first step. Now, if only finding a reputable breeder was as easy...
Unfortunately, you cannot tell if a breeder is reputable from looking at their website.
Tips for finding a reputable, ethical golden retriever breeder:
Here is a link to the Golden Retriever Club of America website detailing questions to ask potential breeders.
Here is another link to the Mid-Florida Golden Retriever page about what to look for to find the best puppy and breeder for you.
Do not feel embarrassed to ask a Golden breeder to provide you with copies of health clearances for the sire and the dam of the litter!
In fact, this tells me as a breeder that *you* are an educated and informed puppy buyer and nothing makes me happier than families who LOVE to do their research!
The best way to identify a reputable or ethical breeder from one who is less so is to check for annual clearances on all of the dogs in their breeding program (especially the parents of the litter you are thinking about) via an advanced search on the Orthopedic Foundation for Animals website (link to advanced search).
To do this, go here and type the dog's registered name. Importantly, their registered name is not the same as the name you may know them by. That's their "call name." Registered names should be rather long and start with the person's Kennel name. For example, Cora's registered name is Golden Hour's You are My Sunshine.
See if any results come up. If not, that is a major red flag. If results do come up, click the dog's link and see what the test results are.
For hips, you want to see Good or Excellent (ideally not fair, definitely not borderline, mild, moderate, or severe).
For elbows, you want to see Normal.
For heart, you want to see Normal Ausc+Echo
For eyes, there should be eye exam results for every year. You want to see Normal. Some results (e.g., "with BO") are ok, it just depends and should be a starting point for you to discuss with the breeder. The importance of annual eye exams cannot be overstated. Goldens are susceptible to certain diseases (e.g., pigmentary uveitis) and the only way to find out if they exist in a genetic line is through annual eye exams.
Also, check for genetic testing. It is important that both parents were tested for genetic diseases goldens can be susceptible to so that two carriers are never bred to each other. Ideally, genetic testing by UC Davis or Embark is considered the gold standard for testing with our breed.
Finally:
Does the breeder list the full 5-generation pedigree of the dam and sire on k9data (the pedigree record keeping source for golden retrievers) if requested?
Fun fact: If you look at the pedigree, you can actually see the clearances for all dogs 5 generations back, as well as how long they lived! (Let me know if you want to know how... it's a bit complicated but can easily be done)
Do the dam and sire have titles on both the front and back of their registered name? (Titles before the name indicate conformation titles, while titles at the end indicate obedience, agility, field, hunt, and other titles).
Are the parents AKC champions?
Fun fact: AKC sets a point structure to only allow a certain number (for example, 250) of champions in a breed every year across the entire country. Puppies from litters where both the sire and dam are AKC Champions or Grand Champions show an elite level of adherence to the Golden Retriever Breed Standard.
UKC and IABCA conformation titles do show a record of conformation, but not nearly the same degree as AKC. I personally value the "CCA" (Certificate of Conformation Assessment) title over UKC or IABCA.
Has the breeder established a track record of raising sound puppies? Ask for references!
How many litters do they have a year?
Reputable breeders typically have one litter every year or two, though there are exceptions.