The good news: you don't need expensive gear for your first lesson. Most good riding schools provide helmets and will let you start in regular clothes as long as they're practical.
What you do need is a pair of close-toed shoes with a small heel — this prevents your foot sliding through the stirrup. Trainers or sneakers will usually work fine.
Clothes That Work
Long trousers are the best option for your first ride. Jeans work, though they can chafe on longer rides. Leggings or fitted joggers are ideal. Avoid shorts — your inner legs will rub against the saddle.
On top, wear something comfortable and fitted. Loose clothing can catch on equipment. A fitted t-shirt or polo is perfect.