You have gotten a bunch of reasonable advice so far but it's time to put in my 2 cents worth.
Personally I find any headlamp more trouble than they are worth, but to each his own.
As far as getting a gun goes a lot will depend on what support in the form of spare shafts and parts is available in your area. Biller and Biller clones have pretty much taken over the Fla market and are quite suitable for that area. OTOH they are pretty much absent from the Oil Rigs as they are unsuitable for a significant "power up" by going to larger and shorter bands. On the rigs JBL HXD series guns and Riffes seem to rule. Freedivers tend to use slightly different gear tuned to their hunting style and prey species, both of which will be different than what and how you'll be hunting. Listen to any experiencd hunter, but
always consider the source.
In the over 37 years I've hunted underwater there is one basic truism to underwater hunting. Whatever gear is tuned to a specific area will be less than optimal 150 miles down the coast! See what gear the experienced hunters in your area are using. A day spent at a local boat ramp observing who has harvested good fish and what
they use in your area can save you a bunch of bucks. I've hunted both fresh and salt water, with experience in most water types and clarity with prey species ranging from a few ounces in fresh water to over 100 pounds on the Rigs.
This will be disputed, but a year spent hunting with NO gun will do you good even if you will be a bit frustrated. Starting with a Hawaiian sling will teach you more about stalking, prey behaviour and patience than 5 years with a gun. It also prohibits you from "practicing your mistakes" as your mistakes will cost you meat with a sling that you might have landed with a gun. They do take a lot of practice to learn how to use, but experience with pistols or a bow will shorten the learning curve. I still prefer a sling for shallow reef fish and lobstering, and I have a closet full of guns to choose from. Sling shafts are wonderful bug "tickle sticks" for the east coast of Fla south of WPB.
FT