What's the best way to fix the sides to the shelves? Would you just
butt them together or should I be routing/mitering bits out?

IIRC chipboard likes coarse screws like those used in plasterboard, so
I could just screw through the sides. I am not too worried about
having screws on show. I could always tidy them up with caps.

I use black PB screws, having tried the SF carcass screws and decided
there ain't much difference.

Or would you do something more elegant with hidden dowels?

Is there a magic method to make sure hole and shelf line up or is it
just a case of measuring twice, drilling once?

If you're having supports between the shelves, use a couple as
"spacers". Clamp them to the side pieces so that the shelf is kept in
position for fixing. For heavier loads you can fix the supports to the
side pieces, thereby creating a groove for the shelves. Main thing is,
the pieces have to be precisely cut so, unless you have a chopsaw, I'd
get them cut to size at a merchant.