I personally don't look at whether or not a certain casino has won an award, didn't even know such things existed, to be fair
Whenever I choose a gambling website there are 3 things that matter the most to me:
1. Provably fair. I like to be sure there'll be no scam.
2. Nice interface, navigation. Sometimes it can be really hard to find something on a website, that wasn't designed well, that can be very annoying!
3. Reviews. Some of the websites can buy themselves good reviews, no doubt in that, but mostly, in my experience, if there are some flaws and pitfalls - at least some reviews will tell you about that if you do your research.