I answered previously from my phone. I'll expand a bit now that I'm on a real computer.
Generally speaking, for all sporting activities, equipment which physically touches your body should be prioritized. Examples would be boots for snow skiing, shoes for rock climbing, and masks for diving. A poorly fitting mask will consume your attention on every dive; any "economy" is false. Buy once, cry once.
I put wetsuits. smurf suits, and other exposure protection in a side category. If you need them, you probably really need them so they are prioritized automatically for that individual. YMMV.
After the mask, I said an AI-optionable computer should be second. Lots of opinions here about that, wondering why folks can't just use the SPG, too distracting to newbies, etc. Here's my reasoning. First, it makes it easy to keep a dive log. It's very easy on busy days to not record various parameters, by the end of the day you're tired, by the next day you're busy with THAT day's dives... and pretty soon you lose track. Having a history of what you've done, and when, helps all divers better manage their "career" and progression.
That data capture leads to the next reason: The ability to see trends in one's diving behavior. This is why AI is important, if not immediately then later when you get your own reg set (#3 on my list). There are countless threads here discussing air consumption vs. this-and-that, recommendations about improving breath management, discussions about NDL's vs. depth and time curves, and related topics. Yeah, you can do a bunch of hand-wavey guesses based on glances at an SPG and analog depth gauge, but nothing beats the ability to look back in time and see how your SAC has been changing, how fast, and over what period of time. Be honest - you won't remember to write all that down after every dive, it will be forgotten, and so you won't have the data.
Renting a computer is useless. As others have noted, nearly all of the time you won't know that model so all you really have is a digital version of the analog gauges which, as noted above, have no data capturing value.
So: Computer is #2 after body-interface items like the mask. You get dive logs that keep themselves (even if you don't take the time to add notes later), you have a device you're actually familiar with (and so will actually use), and as you venture deeper and longer you gain an extra layer of safety and insurance.
If you don't have your own reg set, get a computer that supports AI as a later option. At least you're capturing, and learning from, what data is available - and you're ready to capture and learn from air consumption info once you add the AI transmitter.
When we go on "non-diving" trips we still bring our masks and computers, which easily fit into our backpacks or any size luggage. Compared to our full kits they add very little volume and weight, but if we get a surprise chance to dive (which has happened many times) we have the top two pieces of personal gear with us.
Having your own reg set and BCD follows closely behind having your own computer. Obviously the reg set is truly life support equipment whereas the computer is not, but as others have noted there is maintenance involved. Newbie divers may not dive enough to maintain their regs, raising the possibility that ratty rented gear may actually be in better operational condition than their own!
The above comments are for those trying to minimize how much personal gear they have to buy. Now I'll share a story about equipment confidence. A few years ago my wife, my son, his girlfriend, and I were off Barbados (which we LOVE). We did a nice wreck dive together, but the surface was choppy and when it was time to go back out after the surface interval the girls opted out. My wife said to our son "Here, use my gear instead of the rental stuff", which he did. At dinner that night my son suddenly said "That dive with Dad today was the best dive I've ever done". We've been to some pretty awesome places and while that dive was absolutely spectacular, I didn't expect that kind of reaction. We asked why, and his response really taught me a lesson: "That was the first time I've ever had complete confidence in my equipment. With rental gear I'm always making sure I'm near someone and their backup regulator. Today was the first time ever that I could relax, because I knew for certain Mom's gear would work because I know you guys maintain your equipment. I could enjoy the dive."
I had not realized how stressful and distracting unknown gear could be to someone. I made a promise to myself that the next time we go on a dive trip with our son, he'll have his own kit even if it's an early Christmas present. I want him to know that his equipment is in top condition, so that while still being an Alert Diver (tm) he can stop worrying and enjoy the experience.
Moral of the Story: If you're already spending all that money for dive travel to some destination, make the investment in a full kit for yourself. It's a one time expense that will make that, and every future, trip better.
My $0.02, YMMV, standard disclaimers, IANAL, etc.
