Let's say a bitcoin casino, what makes you deposit bitcoin?
Is it the provably fair? Does it mean you trust a site when the game is fair?
Is it the looks of the site? The amount of users there are? If there is an open chat where you can see active users?
In the case of casinos, I can't tell you what criteria you should look at because online casinos have anonymous owners, but I think looking at their thread in this forum can give you a clue whether or not to trust the online casino.
In the case of exchange I use exchange that I know the owner of the exchange is not an anonymous person, and I always try to know where is the headquarters of the exchange
in the case of bitcoin wallets i use the wallets that have good feedback from community members
Another question: What does a new service need to earn your trust?
if is a new exchange should not have anonymous owner and should have headquarters
if is a casino I think should have good community feedback