I'd like to begin learning Ramban Al HaTorah and was wondering if someone has had experience with learning Ramban using a certain set of Chumash. I know of three different sets that have biurim/notes and was wondering what the differences are between them and which anyone has found to be the most helpful.
I have learned Ramban al Hatorah with a chavrusa this year. I used the third set you linked (Chavel Ramban, Mossad Harav Kook), and my chavrusa used the first one, the Tuv Yerushalaim set. Tuv Yerushalaim had commentary that was slightly easier to understand, but also skips commenting on any sections that are Kabbalah-heavy. If that's not a focus for you, I would recommend the Tuv Yerushalaim for a beginner. I have no experience with the second set, the Oz Vehadar, but if it's anything like their commentary in their Mikraos Gedolos, it will be extremely comprehensive.
A few other notes:
I would not recommend learning Rabbeinu Bachya/Bechayei alongside Ramban, as he is an independent commentary, and often even harder to understand. If you wanted to learn a relevant commentary, I would suggest Rashi or Ibn Ezra, what the Ramban often quotes and disagrees with. Alternatively, you can learn the full commentary of the Tur, which he himself says is based on the Ramban, and may serve to help explain the Ramban in a few sections.
This is really more of an opinion-style question and may end up getting closed as off-topic.
But if your objective is to understand what Ramban teaches, any one of the newer, complete and accurate texts is good. My preference is the Rav Kook edition which you linked to.
In general, when learning Ramban to the Torah and especially over Bereshit, it is a good practice to learn side-by-side for contrast and comparison, Rabbeinu Bahya ben Asher. Rabbeinu Bahya was a student of the Rashba, who was a student of the Ramban. So the context is appropriate. There is also a Mossad HaRav Kook edition for that too.
And if you are looking for any additional clarification, include the super commentary, HaEzrach B'Yisrael by Rabbi Yisroel Yitzchok Koronet which clarifies Rabbeinu Bahya.
This is a wonderful initiative. I am doing this as well, using artscroll's 7-volume elucidation. Since you are mentioning 3 Hebrew-only chumashim, you might not want English.
But I have something else which might prove very beneficial to make the task more manageable in a first pass. There is a list of the most important Ramban al ha Torah commentaries which someone has compiled (I uploaded it here), sorted by parasha, with a short index on the last page.
PS. Unfortunately I do not know who the author is. There is no copyright information I found either.