I thought italics were pretty standard.
I would never use quotes, since I know I would read it as speech.
Depending on how it's written, nothing might be needed, and I'm not particularly fond of large italics paragraphs just because I don't like the way they look, but for lines of thought here and there I'd use italics. Same for emphasising words, which is somewhat apparent as I just did that above, and do so all the time in written communication.
Funny, for first person is generally when I find even less need for designating thoughts than 3rd. The only time I think I've done it is when my MC was really, really anxious, and his immediate thought blended with the stories.
Something (roughly) along the lines of:
"But why? What do you want me to do? Why do we fight?" he says. He must be new at this, he must be. He's too attentive to me to notice the guy coming up behind him with the knife. Slice across the neck and he's gone. Because otherwise that'd happen, stupid. But I don't have time for him, I have to keep moving. No one's catching me.
^^ Maybe not the best example, but that's more or less how I'd do something like that in 1st person. 3rd person I find I don't need too many direct thoughts, though when I do them I just write the thoughts and italicise.