Transmute Artifact
Sorcery, UU (2)
Sacrifice an artifact. If you do, search your library for an artifact card. If that card's converted mana cost is less than or equal to the sacrificed artifact's converted mana cost, put it onto the battlefield. If it's greater, you may pay

, where X is the difference. If you do, put it onto the battlefield. If you don't, put it into its owner's graveyard. Then shuffle your library.
So above is the current oracle text of Transmute Artifact. However, I have a few question as to how exactly the ordering of certain things go. Thank you for any replies!
1. Am I right in saying that sacrificing the artifact is not part of the cost? That is, if Transmute Artifact is countered I do not sac an artifact?
2. After Transmute Artifact resolves, I need to pick an artifact to sac. Can I tap the artifact in response to that? Let's say I want to sacrifice a Mox. Can I tap the Mox after Transmute resolves but before choosing the artifact to sac, or must I float the mana before I cast Transmute Artifact? So for example, I want to Transmute Artifact a Mox into a Voltaic Key. Do I have to tap the Mox before casting (and potentially telling my opponent what I am going to choose to transmute for before the spell even resolves?) or can I leave that vague and do it after?
I hope I made my question clear. It does make sense to me but it's 2:30 in the morning and if you need me to explain it better just say so and I'll try my best.