When Voldemort tried to kill Harry he was (according to Dumbledore, and common sense) planning to make his last Horcrux. So what was the important (magical) artifact Voldemort would have used? Why didn't he use it when he came back?

Aye, I know he didn't went in. But I couldn't have know that after book 6. That is when I Thought he would go there and find a powerful magical artifact (probably from Gryffindor), and that would help him somehow.

But wouldn't it make plus sense if it happened because Voldemort already prepared everything for it? Plus, he always used important death for them...what can be plus important than killing the one person who might be your downfall?

Exactly, it seems to me that Voldemort would indeed make his final Horcrux after killing Harry. And since it is a complicated piece of magic, it make sense that Voldemort already made preparations for it. And that is the reason it was possible that a Horcrux could be made par accident. And it is also true that it is necessary to kill someone before a Horcrux can be made. And it happened to be that he had just done that (twice).