Welcome to the forum, and welcome to collecting. In my view the factors you listed all matter, but I would rank them in this order when you are starting out.
First, buy a watch you genuinely enjoy wearing. A first piece that sits in a drawer because it does not suit your wrist or your daily routine rarely becomes the start of a collection.
Second, look closely at the movement and the overall condition. A well-made, clean movement, an honest dial, and hands and a case that match the period of the watch usually matter more for long-term satisfaction than a famous name alone.
Third, consider serviceability and provenance. Ask whether the watch can be serviced, whether it comes with its papers or box, and whether the seller can explain its history clearly. A clear, documented history protects you far more than a bargain price.
Finally, take your time and handle as many watches as you can before buying. Visiting a dealer, trying different case sizes, and reading older threads here will teach you more about your own taste than any single recommendation. Good luck with your first piece, and enjoy the search.