I learned how to dive while I was in Panama City FL for work. I knew I was hooked immediately but I also knew that I hate the cold so I would be a destination diver. Obviously, while on the course, I used the gear that was supplied by the dive shop.
When I got back home, however, I went in to the local dive shop and I had a full set of gear before I went on my first trip. Here was my logic: If I rent, I would be paying somebody and getting nothing that I would be keeping for my money. I would also have no idea how well (or even if) the equipment was maintained. Even if I bought entry level gear (which I did) and upgraded relatively quickly (which I did) I would have my own gear. I would know how it was maintained. I would become familiar with it and I would know how to use it (especially the computer).
My LDS was a Sherwood dealer, so all of my first purchase was Sherwood. I got a Cayman BCD, a Brut reg and a ReSource Dive computer. The BCD was a jacket style, and I soon found (one trip) that I didn't really like it and I switched to a back inflate style. My "Brut" reg was aptly maned. It was "bullet-proof" and I used it for several years until I switched it out for a Sherwood Maximus. Much like my BCD, however, I never was terribly impressed by my first dive computer and it was replaced after a couple trips.
So, after my first trip, I had decided that I disliked my BCD enough that it needed to be replaced immediately and I wasn't impressed by my DC.
Did I regret buying my gear right away?
No. Not really. Diving is a learning process. I stand by the decision even though I wound up replacing much of my gear fairly quickly. I learned that I and I alone was responsible to ensure that my gear was maintained. I knew that it was done "by the books" and if there were any problems, I knew that they were addressed before I used the gear again. I knew that I would be using a DC that I was familiar with and that knew how to use. There was never any doubt about whether I was getting well maintained gear or whether the mouthpiece on the reg had been properly dis-infected since the last time it had been used. (I really did not want to get "cooties" from the last person who used that reg.)
There are advantages and disadvantages to either owning your own gear or to renting it at the destination. I can tell you what I did and whether that worked for me, but ultimately you will have to read the posts, and make up your own mind as to what you believe will be best for you. There is no right answer, and there is no wrong answer, but for each person there is an answer that is better than the others.
Good luck and have fun!