In exchanges, withdrawal process should be fast and good support, for gambling sites almost same withdrawal,team have many features. The UI is another plus but as long as they are legit registered company then it's a good start, before I try new potential service by putting small starting capital to test, but now due too many scam,kyc and phishing sites, if it's new project it's better to read reviews here in forum as many might already tried it.

Quoted and verified

However, I would like to point out that your message is actually factually incorrect and somewhat misleading. That is NOT a SegWit address. It is a legacy address

Not sure where you got that signed message template from... or why you chose to use it if you're not actually going to use a bech32 segwit address as per BIP173

So it's an online wallet, I must warn you that this is generally a very bad idea to use online wallets as a stash for your bitcoins.
There must be some sort of a bug with it because I have used 3 different services, including my electrum, to check your signature. All of them failed to verify with the address you provided. Please, for your own safety, use dedicated and stand-alone wallet programs like electrum.

Message verified to be from 1PJRESYZzXmArdrLeGRn1ZcdMusYiDTaAu
Are you sure you copied the correct address? 

it starts by their history. for example if the service is an old one you can easily look at some feedback on this forum or elsewhere to see what other people's experience with that service has been like. if they scammed any of their users, if they were gotten hacked, leaked any personal information of their users,... and a lot more. with a quick search you can easily figure out how much trust you can put in a certain service.
for instance an exchange service that has been hacked before and has poor customer support deserves a very small trust from traders.

then it is a matter of how much risk you are willing to take. for example the gambling site you mentioned, you can verify their fairness and history and then decide if you want to trust their honesty and for how much.

One of the main reasons is that you can see the site's funds. It's all public. Most of the sites share their addresses, even if they don't, you can basically find it by just checking a few addresses on the blockchain. This is especially important when checking out, for example, an exchange site. If the exchange does not have even 1 BTC but is advertising themselves as the biggest and the best exchange, that should raise some flags. So, long short story. Transparency, whether they like it or not is probably my main reason.

It varies depending on what type of service do they offer. For casinos, must have is the provability of the fairness of their games and their withdrawal/deposit system. Customer support is a factor too, and if they failed on this side of the service, usually it makes me want to go turn my back and just forget that they exist. Same for all the other services. If they failed on customer relations, they might as well fail on other aspects because they don’t listen to the customers’ concerns and would likely not want to change or improve what’s weong on their service.

Aside from the very simple design which is not attractive, there is also a big missing thing in this site. It is about the provably fair system, I cant find anything related to how the coinflip works which should be the most important thing in this kind of game. Without provably fair system, there is a high chance for cheating attempt.
The available games to be joined seems to be made by the admin to attract users but it wont work. I believe no one will spend their money on a non provably fair coinflip game.
One more thing, fee for instant withdrawal is so high (1000bits = 100k satoshi).

Maybe you can give some demo account for people to try before they deposit some balance. You need to work hard if you want to make your site bigger and could attract more gamblers. Many things that you need to fix but that is okay since it is just a beginning for your site. But the best you can do to attract more visitor is placing the faucet so people can try with free coins to play.

But I think I have a problem to register on the site because I see "Your password has to be at least 4 characters." And I use 10 characters with a combination, but that message still appears.

On the downleft corner of your thread (scrolling all the way down), you will see two links: move topic and lock topic.

Perhaps is better to move your thread to a more specific section, like this one.