When I was in your position, I ended up buying a package with a BCD, Regs and Computer. While the Regs worked great for me for 6 years and as Kamala said are a key piece of life saving equipment, that would be my next thing to get. You have no idea when the rental ones have been serviced last. And that is the key. Keep them serviced regularly and they can last forever.
On my BC, I bought a jacket similar to what I used in training and it just was too bulky for travel, after a couple of years I switched to a Backplate/wing and haven't looked back.
On computers, clearly if you start diving on these SingleDiver trips, try one of the Cochran's before you buy. You mentioned going wireless and I have a setup like that as well, but that can come later. Mine is a wrist mount so nothing dangles. But I still dive with a gauge that came in handy when after 4 years the transmitter suddenly stopped working in the middle of a dive trip.
Keep it simple at first and you can add complexity later as you figure out how often and what type of diving you are going to be doing.
Thanks for the info! Yeah, I think the key is try before buy on the bigger ticket items. I'm gonna work with Kamala and see what we can do.