The safest casinos could mean one of many things. First of all, there are two types of casinos; physical and virtual. Deciding factors on what is safe between these two is completely different. While they have the same basic principals, the two types of casinos are worlds apart. But, in this site we are dealing with internet casinos, so we will skip over Vegas.
Safest Casinos Online
The safest casinos online are the ones that are government regulated. Then, if you want to take a step up, you look for casinos that are members of the Interactive Gaming Council. These two entities regulate online gambling, making it safe for all users.
Your money is a major concern. Find out what system they use for taking deposits and issuing payments. If you have not heard of them, look them up. Try to stay with a big name. They have criteria for customers they will take on. No major payment company wants to be linked with a questionable casino. Therefore, if it is a big payment company, such as PayPal, your safety increases (don't use this as a main determinant).