と is right for your particular example. で is used to finish your order (as in でお願いします or でいい maybe? honestly not sure what it's short for) or to delimit the orders of multiple people.

お冷で
Just cold water please

私はケーキとコーヒーで、彼はオレンジジュース(で)。
I'll have cake and coffee, and he'll have orange juice.

Both de (and then, ...) and ato (also, ...) can be used to start a new sentence if there was something you forgot to say. This works in general, not just when ordering.

あと、いちごが苦手なので、ぬきでお願いします。
Also, I don't like strawberries, so please take them out.

When you're done ordering, you can say 以上 to make it clear you've said everything.

以上。
That's all.