My personal order (specifically for travel divers to warm-water locales):
1-
Mask (spend time on this; it should be so comfortable and effortless that it is invisible).
2- Boots/booties and
Fins that fit over them comfortably.
3-
Wetsuit/exposure suit that FITS and is comfortable
for you in the temperatures you will be diving most often (expect to be donning and doffing a lot of ill-fitting suits....).
4-
Dive computer (a basic inexpensive one, non-AI) and learn how to use it.
At this point in the scuba journey, purchase nothing further until the diver logs at least 100 dives. By this experience milestone, they should have both a) strong preferences in what they want in the remaining equipment, and b) recognition that a lot of the remaining gear is jaw-droppingly expensive new, and that the gently used market is - generally - the way to go.
5-
regulator set (1st stage, primary air source, octopus/octo-inflator, inflator, SPG (yes, get an SPG even if your computer is AI)
6-
AI dive computer (sell the original one, or keep it as a backup) and learn how to use it.
7- travel friendly
BPW or BCD (but let's face it, you're getting a BPW by this point

).
8-
torch
9-
save a dive kit w/ basic tools
10-
SMB & spool and learn how to use it
11-
surface whistle
What you DON'T need (again, based on being a travel diver):
- compass (unless you plan to dive regularly without a DM or guide, (Bonaire)).
- knife/cutting tool (that knife strapped to your calf makes you look like a twit).
- noise maker (do you enjoy diving alone? you will be if you insist on being the noisy diver).
- slate/writing tablet
- camera/action camera (this inevitably turns the expensive hobby into a very expensive hobby. Ask me how I know...

).