Thank you for writing. Frankly, I'm somewhat overstretched now given the students already working under me, but I may take one new student next year. Allow me to be specific and clear so you can decide how best to proceed.
Different faculty members operate differently. My usual practice is to shortlist and interview about three applicants after the Main Round has closed, and take in one of the three.
If you like, you can send me right away a short one-paragraph statement of your area of interest, plus a short sample of research (don't rewrite anything; just send something you already have finished/published). I will read them and tell you either (1) our interests are too different for me to be a suitable supervisor, or (2) there is some chance I may be able to shortlist you, though it's not guaranteed.
If (1), you should still feel free to contact other faculty members whose interests are closer to you. If (2), you can list my name as one of your potential supervisors. Nonetheless feel free to include other faculty names as well; I don't mind as long as you think that may enhance your chances -- it might.