A professional studio will use full hospital sterilization and disposable items for your safety.
There are virtually no health problems related to professional tattooing. There has never been a single reported case of tattoo related HIV transmission. Reports of hepatitis are rare and equal to the numbers you would expect from any other segment of the population - there is no specific connection to tattooing.
Historically, even the dirtiest of tattoo shops seemed to deliver a safe product and this is why there were very few laws regarding tattooing or piercing. However, it would make sense to do what you can to avoid shops that are dirty, who reuse inks and needles, do not sterilize or practice good hygiene.
Why would you want to trust your health and your permanent art to someone who does not show consideration for your feelings of safety and security? If they care that little about your safety and feelings before and during the service - how much will they care about your satisfaction after the service?
A good studio will be very open and willing to discuss the health precautions they have taken and will want their safety equipment to be visible and in use. It should be obvious to all prospective clients that they are in a safe place.
You might have to travel a little farther or pay a little more but you will be happier with your product and service. Your health is important – don’t take chances with it.