I pick colours, shapes and sizes that look interesting. I have worked with different stone hardness from nail scratching Soapstone all the way up to chisel blunting Black Granite.
The way I pick a particular stone depends on three things:
1) I look for a specific size and shape and sometimes colour that will accommodate an existing idea.
2) I find a stone with great colours and a big enough shape that suggests what might be trapped inside and I work towards that idea until the stone suggests something else.
3) I find a great stone with amazing colours and haven’t a clue. So I buy it and look at it for a few weeks, months or years until I know what to do with it.
Of course there is always the old “standby”.
Buy it and drill a hole in it. The visual feedback of that first cut, will get you started on how it will progress.