I can only give some general advice here as I shoot Nikon, not Sony.
First, I would suggest you actually rethink how you are thinking about this in terms of cost. It's just frighteningly expensive, even to go 'cheap'. If you are price conscious, look to the used market. Not sure how many used housings you'll see for A1's though as it is pretty new still.
The traditional 'cheap' housing is Ikelite, and you need to research any limitations there. I've not used one.
I have, however, bought 4 Nauticam housings, and I like them very much. But costs are double + more than an Ikelite. To some extent, the housing you buy can depend on the country/area you live in. Aquatica is a Canadian company that makes good housings. Isotta is Italian, and Subal is Austrian. Nauticam has a strong US presence. Can make a difference in both availability and ease of service.
Besides the housing, you need appropriate ports for appropriate lenses. For me, with Nikon, the choices are few - 105mm macro for full frame, maybe 60mm macro for DX. 16-35/14-30 for wide rectilinear zoom, and at least for f-mount, 8-16 fisheye.
If doing wide rectilinear, you are looking at big, heavy dome ports, while fisheyes get away with something half that size. A big dome port can dominate how you have to travel, by the way.
Then you need lighting, meaning at least one strobe for stills, and probably two lights for video. You can probably find lots of used options here.
None of it is cheap. Here is a new package from Bluewater that seems reasonable to me. (I just paid $7500 for just the housing for my Z9).
https://www.bluewaterphotostore.com/nauticam-sony-a1-housing-strobe-package?setCurrencyId=1&gclid=Cj0KCQiAjbagBhD3ARIsANRrqEuRXfZYI0SqMguqRvw4SbYfyad8tVqddwonnaZ1EGJS58JkNHkwPaoaAjfOEALw_wcB
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Phoenix Arizona Craig
www.cjcphoto.net
"I miss the days when I was nostalgic."