I am going to give you an idea of what I look for in a stud. I have 2 female german shepherds that I am trying to breed for my first two litters. This is after working with the breed for well over 10 years. Both of my females have 'a' stamps for hips and elbows (the german equivalent of OFA), DM tests, have a conformation rating, and are titled in IPO and SDA. IPO is tracking, obedience, and protection while SDA is obedience and protection. I do all of my training and trialing. This is in addition to a strong pedigree.
Both of the males I picked both have those health tests and titles also. One was on the world team and won multiple IPO championships.
Basically if you have a dog that you want to put up for stud, you need to have something special that people with quality dogs would want. As a bare minimum, official hips and elbow are a must. The dog must also have a good pedigree which take experience to know if it does. I personally wouldn't breed to a dog without titles because it shows dedication of the owner and it shows the strengths and weaknesses of the dog. There is no perfect dog, and it is important to know what needs improvement. Then there is also temperament, other health problems, and conformation to consider.