How do I work out how many U of cabinet space I need?

Add together the rack space required by everything you intend to mount: patch panels, switches, shelves, horizontal PDUs, cable managers and any other rack-mounted equipment.

Then consider equipment sitting on shelves. The shelf may occupy 1U at its mounting position, but the equipment resting on its platform may extend through that U and require additional clear space above it.

Finally, leave some room for growth if possible. A cabinet calculation that arrives at exactly 12U for a 12U cabinet is mathematically impeccable and operationally rather optimistic.