I need a grammar (English) expert?

Grammatically they are both correct and socially acceptable. The only different is that "while we were eating, the phone rang" would be an example of an introductory participle clause while "The phone rang while we were eating" would be an example of a medial participle clause. It's where the conjunction is placed. Maybe you can describe it in the subject matter. Like, if you're talking about dinner, you would say the first one. If its the phone call that you want to talk about, use the second one.