Without fancy gizmos how can I locate the sturdiest part of a stud wall to hang a kitchen cupboard?

use the age old tapping method,clench your hand together and gently knock the wall along ,you will hear a variation in tone hollow to semi-solid,the more solid the knock is where your studs are,to double check tap a nail lightly with a hammer in the spot ,you will then find it hits the solid stud ,these studs are usually plumb so just mark with a pencil and level,hey presto stud detected without fancy gizmos ,

You will never find a timber stud in the exact place you want to fix a bracket for a cabinet ( if you do go buy lotto ticket) Best way use spring toggle fixings or else mark where cabinet goes, where hidden cut out piece of plasterboard and slide strip of ply behind & fix then refix plasteboard . if you have run of cabinets cut out strip an fix long run of 12mm ply ( same thickness of plasterboard) to studs . Make sure you measure down from top to centre of fixing brackets.