Linux will probably come out first
That’s more than fine by me, I rather included MacOS for fairness sake.
I plan to implement all of the things you’ve mentioned
Are you sure though that you would want to keep DX, OpenGL and Vulkan up at the same time? My suggestion would be to go for OpenGL for now, as it is supported on all major platforms and goes far back in compatibility, and porting from that to DX and Vulkan would be much easier than in any other direction between those three. At least if memory serves correct.
Also what are your thoughts on making sure your game works in Wine so long as there are no native builds? Would that be something you’re interested in now or is that all later?