Used fixie or new build

Hello. I am new to fixed gear riding. I’m looking to get a bike to start, and I was thinking about either buying a used or prebuilt one or building one. Below I have attached a screenshot of one that I found on Facebook marketplace that seems like it is a good deal, and attached the document where I have the build that I would be planning to do if I were to build a fixed gear bicycle in the comments. Let me know what you think!