Well I used to get this all the time with pushups, so I wouldn’t worry.
just think about it… your wrists wont be used to being put in that position, especially if you’ve just started doing it. It’s awkward and you’re putting basically the whole of your body weight though that tiny load of joints, so yeah, you should expect a bit of soreness, nothing to worry about I’d say.
If you start to get bruising though, or you find that moving your wrist is physically hard and VERY painful, then you should stop and use RICE :) (Rest Ice Compression Elevation ;) )
Personally I go for the hands facing at 12 o’clock at just less than shoulder width, but thats what’s comfy for me.
Just do what feels right for you, it wont drastically effect the muscles you use, just it can make it harder or easier as the muscles have to ‘twist’ as well.