You can wear any comfortable clothes that are suitable for light exercise. Trainers are good and so are any other lightweight foot coverings. You should NOT wear flip-flops or open back sandals.
We generally recommend against this. The venues that we train in are used by multiple groups and there is always the danger of dirt or something potentially dangerous being on the floor.
There is no requirement to buy special clothing. We don’t even have a club T-shirt (although we are considering the idea - it would look ‘Cool’).
There are lots of different styles (and sub-styles) of Tai Chi, so if you are looking to learn the style that we teach, you will need to look at our videos and come to our sessions. However the Yang 24 form, which is probably the World’s most popular Tai Chi form, has lots of people demonstrating and teaching it both on YouTube and via commercially available DVDs so any of those will probably be OK. Also looking at videos of people doing ANY form of Tai Chi should be interesting and hopefully stimulate your interest in this wonderful art.