unless you're a big dj making a statement that you've arrived and you're on the decks then no you should not stop the previous persons record. i find it really annoying when unknowns do it. who the **** do they think they are?

also, i don't think you should ever stop the record then start with something that jsut has plain old beats at the start. a nice synthy atmospheric intro is always nice to hear at the start of a set