Underwater camera setup

I'll pass on some experience.  Might help guide you a bit.  I'm not sure if the camera you want exists these days, particularly at your price limit.  I'd strongly consider used whatever you do, but that too has its own set of issues.

I used a series of Canon point-n-shoots for years, each with its own dedicated Canon housing.  Small enough to dangle from a wrist strap.  Internal flash with a small snap-on diffuser on the housing.  Effective strobe range about 1-3 feet.  Nice thing about these rigs were that they cost under $500 new, for camera and housing.  I still have a working s120 somewhere.

I ended my run of those kind of cameras with a Sony RX100 II, basically a point-n-shoot with a bigger sensor.  I put it in a Nauticam housing and added dual strobes. The only thing that made that rig particularly better was the strobes.  After years of using the Canons without flash, I felt I pretty much had all the green fish shots I ever wanted.

These days that whole class of camera doesn't really exist anymore, or is much more expensive.  But you might find something like the RX100 used for your budget.

Flash - it changes everything.  Can't imagine free diving with it, but can't quite imagine shooting stills without it.  Having an external flash - much less two - hanging off a camera completely changes how you have to dive with it.  Can't really just drop it and let it dangle from a wrist anymore.  And it adds enough drag to really slow you down as well.  (When I needed to move faster or battle current, I'd turn the rig sideways with one strobe by my ear and the other between my legs to cut drag.)

But, stills really need good lighting, and that mostly means strobes at any depth.  Boosting ISO doesn't help when the colors in the light aren't there to start with.  You need to add it.  Video, another story.

In 2016 I moved to a full frame housing for my Nikon D810.  When mention is made that your travel gear will be made up of mostly camera, there's a lot of truth in that.  I have over 40 pounds of dive camera gear, and that's just two lenses and two ports for those lenses.  It's a load above water, and it's significant below water as well.  I can't imagine free diving or surf shooting with anything near this size.  I can't even lift it half out of the water to do over/under shots.