Good news: you already own the right outfit. First-time students regularly lose a week to worrying about this, so here is the complete answer, including the one thing that actually matters, which is on your feet.
Clothes: comfortable, that is all
Wear whatever you would wear to a relaxed dinner: something you can move your arms and hips in without thinking about it. Layers help, because dancing warms you up faster than you expect. Nobody dresses up for lessons at our studio and nothing is judged; the ballgowns you are picturing belong to a different universe than a Tuesday evening in Rozelle.
Shoes: the one thing worth a thought
Ideal for a first lesson: a clean, comfortable shoe with a smoothish sole that lets you pivot, a plain leather-soled dress shoe, a low block heel you can walk naturally in, or a smooth-bottomed flat. Avoid grippy running shoes if you can, because their soles grab the floor mid-turn, and skip thongs, slides and anything you would not briskly walk in. If sneakers are what you own, wear them anyway; your teacher will work with whatever walks in.
Proper dance shoes exist and are lovely, and you should not buy any until dancing has stuck and your teacher can point you at the right pair for your style.
The things nobody warns you about
Bring water. Trim the layers you cannot dance in, like heavy coats. If you have glasses that slide or hair that ends up in your face, deal with both before the music starts. That is the entire list; there is no equipment in this hobby, which is one of its glories.
More useful than the outfit
Knowing what the hour actually holds settles more nerves than any wardrobe choice; what happens in a first dance lesson walks through it minute by minute. Then book the free first session and wear the comfortable thing.