The party is in full view of an opposed group. Maybe they are talking, but there's no question that the other group is there and there is a general wariness that combat may occur but it's not definite. Very important - it is not definite that combat will occur.
One of the people involved declares something that will start combat. "When he insults my family I draw my rapier and stab him." There isn't anything particularly sneaky about it, like a subtle spell.
Do you roll initiative and that person goes where they go? Do you roll initiative but put them at the top? Do you treat it as possible surprise that combat is breaking out "right this second" and do something like roll insight or perception to see which combatants (on both sides) are surprised and not going in a first round? Or something else?
I voted other. I think any way to do this is fine as long as everone knows ahead of time and I have not found a way that is "the best". Some ways are "the best" mechanically, others are "the best" thematically ..... and other ways are best at ensuring you kill the party
When I DM and surprise is not a factor and they are not immediately hostile a player can start combat and that player acts first, gets a full turn AND loses his first turn in order. Basically he beats everyone else on the 1st round and then when it gets around to him on the first round he can't do anything (although his reaction counter does reset). So we are talking to the guard and a player decides he wants to start the fight, then he can and can get the first turn, then we roll initiative - if he gets a 10 everyone else goes once and then everyone with higher than a 10 goes a second time and then he goes again. Theoretically the other side can do this too too, although if the bad guys don't attack on sight it is usually because they don't want to attack so it is rare that they use this. Either side can also ready an action to counter this. So you are talking and one player is afraid a fight is going to break out - "i
f the enemy reaches for his sword I fling a dagger at him". If that happens the reaction goes then the actor that started combat goes, then as above. I limit such readied actions to characters (PCs and NPCs) that are not doing something else. So if you are the guy talking to the guard you can't ready such an action.
If anyone is actually surprised then initiative is rolled and it goes turn-by-turn, whether it is all of them or just one of them. Players can ready an action if they want: Ypu surprise everyone and Rick the Ranger wins initiative and he says
"after Mike the Mage casts his stinking cloud I shoot the closest guy who is not wretching". If everyone on the other side is surprised this can be a bunch of readied actions that happen at once at the bottom of a round.
That is how I run it and it works ok. There are plusses and minuses, but I like it thematically.
Other DMs I have played with run it differently. One one of the current DMs in a game I play is straight initiative. You can't even ready an action out of combat. That is fine.