This is a question I'm asked a lot by beginners, for good reason. In most exercise classes, there is a need to wear specific clothing and footwear, and with some, like Yoga, you might need equipment like a mat and perhaps blocks.
In Tai Chi there's no need for any special equipment, unless you decide to learn a weapon form some time in the future, of course. And clothing wise, all you need are comfortable loose fitting clothing that allows you to move freely.
But Tai Chi is also pragmatic. I practice daily in my garden, whatever the weather. This means that sometimes I'll wear waterproof walking boots and rain wear (even waterproof trousers on occasion). When it's really cold, I'll be wearing several layers and toastie gloves.
It's more important to practise than not.
Although I probably wouldn't recommend wearing stilettos, you can basically wear whatever you like, providing you're comfortable.
As Tai Chi is a slow exercise, it's handy to have a warm top to hand, like a sweat top or fleece, especially when you're just warming up and it's during the winter months.