I prefer to stick with the system for communicating in print we've developed over the centuries. I can't see why the fact it's going up on a screen when we type it instead of on a piece of paper makes any difference at all, apart from making it inadvisable to use underlining as a way of emphasising words, since that looks confusingly like a hyperlink. So I stick with italics, and "quotation marks", with the occasional ! or ... or ?

Asterisks as an emphasising technique is a new one on me, though it seems to be more prevalent than I'd thought, now I've noticed it. I can't see where it has any advantage over quotes. I suppose it's marginally quicker than italics. It has the same effect on me that WRITING IN CAPITALS has on a lot of people. Or writing in green ink in a letter to the paper. The medium drowns out the message.