There is more than one way to correctly present email evidence.
The most common is to print out copies (typically at least four, one for the judge, one for the witness stand, one for you, and one for the other side), and to mark them as exhibits with an exhibit number.
Then, when the time comes to present the evidence you put a witness on the stand (maybe yourself) to testify that the emails are authentic copies of the emails and that the email addresses are associated with the person that you claim that they are. Then you ask the judge to admit the exhibits into question one by one (since there may be other evidentiary objections to specific exhibits).
Often, the other side will instead stipulate to admission of these exhibits since their admission is often a foregone conclusion.
How should I group them? By conversation, by sender/ receiver/
chronological order some weird mix of those options?
Usually, you break them into individual messages, or into conversation groups. There is no fixed rule. It is a matter of what is the most convenient and clear way to present the information. Chronological order is usually more clear, but email threads naturally print out in reverse chronological order in most cases.