Don’t spend a lot of time obsessing about how to relate to the audition panel. Auditions aren’t cocktail parties, and other than avoiding the appearance of being extraordinarily grumpy and crank, there’s not a lot to worry about.
First of all, there’s no reason to walk to the opposite end of the room to shake hands. I know panel members who are firmly against this and others who are mildly irritated by it. Almost no one thinks it’s a great idea, and it’s almost never not awkward. I have no strong opinion, but these kinds of formalities do slow things down terribly. You get a limited amount of time allotted, and you want to use it to sing, not to work the room.
If the panel is paying attention when you enter, it’s perfectly appropriate to greet us with “Good afternoon” etc. We try to greet everyone before they have a chance to wonder what to say/do, but sometimes we get caught up in paperwork. The niceties aren’t compulsory, though – it’s just fine to say nary a word, give your music to the pianist, position yourself by the piano, and then speak.
Most of the time, the panel has your materials. If you need to submit a rep list change (where allowed), often the monitor can handle it. If not, deliver it to the panel with a smile, then get right to the main event.
It is always helpful for the panel to hear your name. If our system is working well, we’ll know who you are; but sometimes things get out of sequence and we get confused. “Good afternoon. My name is Kim Witman” should do it.
If you know for sure that you are to choose your own first selection, announce it. But don’t over-announce it. “I’d like to sing Aria Name” should be plenty. If it’s a rare piece, then expand into “I’d like to sing Aria Name from Opera Name.” But no need to turn it into an exercise in public speaking (as in “I’d like to sing Aria Name, Character’s third act aria in Opera Name by Composer Name). We either have a rep list, and/or we’re smart enough to fill in most of those blanks if we know the name of the aria. You’ll probably just end up getting tongue-tied even if you’ve practiced it to within an inch of its life.
Be efficient and pleasant. Then sing.