Costume Advice - Snape Inspired Look

Hola everyone, I have come to seek some advice for a costume I'm trying to get ready for this Halloween. So I've been invited to a couple of events this year. One is like a murder mystery that is inspired by Harry Potter and another is just a general celebration. The murder mystery one has me playing the part of a character based off of Snape. I have to admit I'm still a newbie to the Lore of Harry Potter but I think I now have enough of a basic understanding to try and attempt this look. I know in the books he is often described as wearing robes but I was hoping to put my own twist on this. Also hopefully this costume will carry over to the later event and still look presentable.

First, I already have a pair of black boots and black dress pants that tend to flow pretty well, so I have a base from which to work with for now. I just need to focus on the upper half a bit more. For a top I was thinking of picking up Tailcoat like this one for starters and then maybe a bit of a cape as well to give it a more flowy feel. This is one hitch I have on what to pick up as I don't know if this one or maybe this one would work. Also, I am thinking I would need a wig so possibly one like this one would suffice? I have to admit that I'm am pretty much a newbie at trying to assemble costumes like this so I'm just trying to get a good feel for this type of thing. Maybe take this as a first step in expanding for future endeavors, since the group that invited me also tend to do Ren Faires so that may be in the cards in the future. Any advice and feedback would be appreciated and thank you all in advance!