Neglected cattelya. Should I repot?

[zerb16]

My grandmother gave me this orchid. She lived in coastal Florida and had it hanging from a magnolia tree in her backyard for years. It is in a clay pot and the roots have grown out and onto the pot. I have no idea what type of bark it is in. I'm new to orchids and really want to keep this thing alive! I live in east TN and have it in a window that gets sunlight nearly all day. Should I attempt to repot and if so, what type of pot and medium should I use. Thank you so much for your help!