How to make a great first impression at a conference?

Don't try too hard. You will have plenty of time later to build a solid reputation.

First impressions are way overrated. They will not be the basis of any serious (as in "costs real money") decisions, least of all concerning some complete newbie.

Enjoy the conference, get to know people, mingle. Play your rôle of newcomer who is just joining the club. Check out what is going on in the sidetracks, you might be quite wrong about their importance (or totally right).

Are the objectives really realistic for the conference? Making your name better known is unlikely in general, given the amount of speakers. I'd focus on finding people with whom you share (research) interests, esp. people who complement your skills in order to do better research. As for highlighting the originality of your research, well, that's overrated IMO. You have to build a bridge to what is already established (which can work as a good contrast to what you did). However, for really new approaches, the reactions might be surprisingly critical. As for catching the attention of a publisher -- not sure whether that's likely. If that's really important to you, perhaps find out in advance which publishers will attend and whether you can talk to them at the conference.

As for being only a public school teacher, sorry, you're not. Or, you're not in that setting. You weren't invited because you teach children, or because of a "pity presentation" (if that is even a thing). You were invited because you did scientific work that is interesting for the community. And you've already got the 'union card' to Academia -- your PhD.

So, frankly, I'd chill and re-think the goals (and the attitude). Like written, it's a chance to meet people with whom you share (research) interests for future collaborations. Have a look at the program and seek out interesting people, esp. on a similar level (PhDs and PostDocs). Reading their papers beforehand might help for conversation starters, esp. when you consider what your (likely) unique "day job" background can offer to their research. Seriously, if it's anything related to social sciences, it's usually extremely hard to find people in a practical setting with whom you can work together, who have access to a good sample. And usually people like to talk about their work (well, some are intimidated by the setting as well).

That approach might make a lasting impression on those people who matter, those with whom you can work for mutual benefit. And these aren't the Elitists. Just be open, and if people look down on you, you know where you stand (in their perception) -- and you know to look elsewhere. And regarding talking to people -- nothing simpler than that (and I say this as an introvert). You share an overall interest in the conference topic and you likely listened to similar presentations. So you have a lot in common/belong to the same group. Not all will want to talk, but if you are not discouraged and try often enough, enough will (and will be thankful for having someone who starts the conversation).

And -- lastly -- given that finding people to work with is still be a very aspiring goal, I'd look at the conference as a learning opportunity. I think too many people go on business card collector sprees on conferences, instead of using the opportunity to find out how the people in your scientific community tick. So don't sweat it -- learn from it, esp. from things that went wrong, and above all, enjoy it.

Everyone starts at the bottom, and no academic of any standing should be put off by the fact that you're a public school teacher. You got invited to the conference, didn't you? Just like everyone else?

That said, spend some time listening first, talk second. Don't try to hit it out of the park. Just get the ball in play and if that leads people to talk more than you believe me, you'll be remembered favorably for it.