PhD Application Email
An institutional email address is not a requisite nor it does make your inquiry looks less serious.
I personally was suggesting a receipt request, but apparently most people dislike the option no matter the purpose. I personally can see the difference between a peer of mine pushing for some action and a student in trepidation. However, as the chance that I would be the recipient is ridiculously low, don't ask for a receipt.
Be cautios and clear filling the subject field. I do suggest something like &quot;PhD openings inquiry, name surname&quot; or so.
I also suggest that the body part shows that you didn't choose the particular recipient at random. This can be very short, at this stage.