For Pilates: You will need to bring a mat with you please. That's all! 
For the Combo: Also have a pair of supportive jogging shoes + your mat (and probably a drink bottle too) 

You can get an el cheapo mat (mine is from Target, you can also get them from Kmart or Big W) or an el luxurio mat from, say, Lululemon (I LOVE these ones).

Just don't bring a camping mat, you dork.

Do try to get a thick-ish one and not the mega thin ones as I would hate for you to feel every bony bit in your butt on every move on the floor!

Wear comfie clothes. Not a fashion parade. Just something super comfie! It's a good idea to wear a few layers too so that you can manage your body temperature easily! 

Our room does not have carpet so a mat is essential.