Three decisions, not one.
A YouTube embed is an iframe pointed at youtube.com/embed/ followed by the video ID. Everything else is configuration: size, URL parameters like start and mute, and the allow attribute that grants the player permissions such as fullscreen and picture-in-picture.
Three things separate a careless embed from a good one: markup that keeps its shape on phones and does not break fullscreen, a privacy setting you chose on purpose, and a loading strategy that does not punish visitors who never press play.
Parameters deserve some scepticism, because a lot of advice online is out of date. YouTube has changed several over the years, including rel=0, which once hid all related videos and now only limits them to the same channel. Snippets copied from old blog posts can carry flags that no longer do what they claim. The ones that work reliably are autoplay, mute, controls, loop, start and end, plus rel, cc_load_policy, hl and playsinline. The generator sets each of them from a labelled checkbox or field, so you never type a parameter.