How do the contemporary sources advise that one starts praying shmoneh esrei of shacharit at hanetz hachama?

I understand that as Halachipedia puts it

The ideal mitzvah is to start praying shmoneh esrei of shacharit athanetz hachama (sunrise).

Question part 1: How precise does one have to be with the time of hanetz? Even where sunrise is observable, if one is a minute after the computed time (on e.g. Myzmanim.com), is that no longer “starting at hanetz”?

Question part 2: My Rav said that there are opinions that it is better to daven a little after the computed time to be sure that one is not davenning before hanetz hachama.

So please tell how the contemporary sources advise that one starts praying shmoneh esrei of shacharit at hanetz hachama?