Of course finding what you like is a matter of buy and try, but there are a few words that will help you on your way if you’re looking for certain qualities in your milk. For starters, the Japanese word for milk is gyuunyuu (牛乳). You might often see something called “Miruku” (ミルク), but this may or may not be real milk. If something is 100% real milk, it will always be labelled 牛乳, and anything else is most likely labelled with 乳製品 (milk product) or 乳飲料 (milk-drink).
Next, you will want to look at fat content. A regular Japanese brand of milk is about 3.6% fat, so you will see this number somewhere on the carton (if only in the details section on the back). A really creamy version might be for example 4.4%, and then a low fat version might be something like 1.8%. Low fat milk is most often labelled like this: 低脂肪牛乳 (teishibou gyuunyuu). You can also find milk fortified with extra calcium (カルシウム) and iron (鉄).
Here are some key words to help you find what you are looking for!
Almond Milk アーモンドミルク (Āmondomiruku)