Great topic, Ronald. I don’t write a lot of dialogue, but I do recall grappling with these issues. Sometimes, I opt for the screenplay format, as I did in this satire. It works if you’re writing a script, but probably not if you try to inline it in a longer piece of prose.
I’ve even foregone quotes and speech tags entire, and written stream of consciousness with interspersed dialogue.
I suppose the golden rule is to be consistent.
Interestingly, I do write dialogue in poetry, where I do keep the quote marks, but sometimes drop the speech tags, for conciseness. Here is an example, this is a translation, verse #7 in particular.
It is also worth noting that the original (Hungarian) uses a different convention for dialogue: long dashes, or “em dashes”. You can see this posted below the English translation.