My $0.02 on dive gear and dive computers...
If you end up loving the hobby and you think y'all are gonna go on dive trips at least once a year, you should definitely consider buying and traveling with your own gear. Think of your gear as essentially your own personal life support system. For me, I want to make sure the equipment I dive with has been well maintained and routinely checked out by an professional...and won't fail in the middle of the pacific ocean. Plus, your own gear, well, fits YOU the way its supposed to as opposed renting some piece of crap that really doesn't fit. Now you can certainly go overboard with super expensive stuff with tons of bells and whistles. For me, I'm actually still diving with the first regulator I bought 25 years ago and it still breathes awesome. It's gets rebuilt by a professional every few years so it still works great. I've been through 6 or 7 BCs over 27 years of diving and I finally found one that I love back in 2016. I prefer back inflation over the vest style but again, that's just personal preference. If y'all get cold easily, at the very least you will want your own wetsuits and dive skins. For serious, people really do pee in their wetsuits, especially rentals. Just sayin.
Computers. I think a dive computer is absolutely mandatory. In fact most dive operators require you to have one of your own or borrow/rent one from them. Dives change depths constantly so you want the computer to keep track of your nitrogen loading for you. As you become more and more experienced divers you will find that you'll start hitting your nitrogen limits before you run out of air. But for now, I'm sure your dives will be air limited. But again, this is a key piece of life support equipment that helps prevent you from getting bent. I feel so strongly about computers that I dive with 2 different ones actually. Does everyone need 2? No, that just my personal preference. And like the rest of the dive gear, you don't have to go with the most expensive one with all the features. For me, I like a more simple interface. Looking at my computer is now muscle memory for me. I want to look at it and know instantly if I'm ok or not.
Hope the training is going awesome. If you ever wanna chat about gear or dive trips over a cocktail, definitely let me know!