This style of dance doesn't need any special gear - most of our students wear casual or business clothes to their lessons. Remember that at heart, partner dancing is a social activity more than a sporting activity, so wear something that would fit in at a cafe, not something that would fit in at the gym. Eventually you'll want to get dance shoes, but dress or business shoes are fine to start with.
Choose long pants that let you take long striding steps comfortably. You don't want them pulling across your thighs, and you don't want them constantly slipping down. Jeans can be okay, but some people find them too hot to dance in comfortably. No shorts, please!
Pick a shirt with enough room around the shoulders that you can lift your arms up freely. If you're coming straight from work it's a great idea to bring a fresh shirt to change into before your lesson. Your teacher or partner will thank you! If you tend to sweat a lot, please wear a thick cotton t-shirt, or else wear a cotton singlet or undershirt under your usual shirt. It's slightly hotter than just a business or casual shirt, but it makes life much nicer for your teacher or partner, who will be holding you as you dance.
Wear well worn-in dress or business shoes that have a leather or synthetic sole - sneakers or other rubber soles will be really hard to dance in, dance shoes are not essential but if you want to buy a pair here are a few dance shoe shops and tips for choosing dance shoes. No Thongs Allowed, for safety reasons.