I wouldn't use "for starters" when talking about food. I would use it if I were beginning a list in casual, spoken English. "Why am I angry? Well, for starters, you arrived an hour late, and didn't even apologize. Then, you....." For food, "for a starter" and "as a starter" are both OK, but I prefer "for a starter"--I'm not sure why. However, I feel like waiters are much more likely to use the word "appetizer" instead of "starter" "Would you like any appetizers this evening?" "Would you like to order appetizers while you wait for the main course?" "Any appetizers (for you) tonight?" And so on.

They are all valid. I don't think there is any distinction to be drawn. Individual people may think about them differently, but that will vary from person to person. If you said any of them, nobody would notice it. In this context, starter is just another word for appetizer. For starters is often used to mean "firstly" or "to begin with," which is why some people might avoid it. However, it can also just mean "for appetizers."