If you like Thai cuisine, Koh Chang is the right place!
And being located in Thailand, you can of course get Thai food everywhere, in restaurants but also from mobile sellers.

Mobile sellers or small local restaurants are quite cheap and the food served can be sometimes very simple but very tasty. Keep in mind that Thai people love to eat spicy, even very spicy. So when you are ordering don't forget to mention if you want it normally spicy (which is very strong for non-Thai people), medium spicy, little spicy, or not spicy at all.

The best time to discover food you are not used to eating is in the evening. Lots of small sellers will come with their bikes or install their products on a stall. Don't be scared to try.
On the north part of White Sand Beach and on the main road, before it becomes dark in the evening, lots of mobile sellers will set their stalls and propose all kinds of grilled food.
If you like sweet food, try the homemade pancakes filled with fresh fruits (pineapple, banana, or mango) and covered with sauce (chocolate, vanilla, coconut milk,... or all together). It's not very healthy, it's very fat but it's delicious!
If you want to try something different, try the fried insects. They look more disgusting than they taste. Worms, ants, crickets, grasshoppers, scorpions,.... they look horrible but they are full of proteins and in fact, don't taste so bad. The worse could be the oil used to fry them.

Otherwise, if Thai cuisine is not your favourite, there are plenty of other types of restaurants. German schnitzel, pizza, burger, pasta, cheese, cakes,... you can find all that you want.
Just have a look at The Koh chang Guide mobile Application or The Koh Chang Restaurants, Bars and Spas guide, they are full of useful addresses!

I can recommend you four good places where you can have a good meal, Koh Chang Paradise Resort & SpaAbella Cuisine, located in Coconut Plaza, Chai Chet, and specialised in Italian food as well as Thai cuisine, and Blues Blues Arts & Food.

In Koh Chang Paradise Resort & Spa, all guests will get 10% Off their meals. They have a large choice of Thai but also European food. In the evening you can get fresh meat, fish or seafood from their grill. It's a beautiful place to have a romantic dinner on the quiet beach of Klong Prao and a few times a week you can enjoy their show made by the staff with traditional dances and a spectacular fire show.
Blues Blues Arts & Food is a very interesting restaurant. You don't only eat original Thai cuisine but you can also enjoy nature and the outdoor art gallery made by the owner. On top of that, it's very cheap and extremely quiet.

When it comes to drinks, the list of bars where to get them can be very long. From the local stores and supermarkets, you can get almost anything. The most famous beer is of course the Chang Beer, but it's also possible to get Belgian, German, Irish,... beers. 
You can also get fresh smoothies, fruits juices, and beautiful cocktails everywhere.