Begin with a design that has been properly assessed for stability, secure joints and the loads created by a moving cat, rather than copying the appearance of a photograph. A large cat landing on a platform places different demands on a structure from an object resting still. Choose suitable materials and safe finishes, eliminate sharp edges and accessible fixings, and consider how the whole unit will be anchored if required. There is no universal screw size or base dimension that makes every homemade tower safe.
If you lack the skills to judge the structure, ask a competent professional or choose a product with clear specifications. A simpler ground-level scratcher or resting area may be a more manageable project. Inspect any completed item regularly and stop using it if movement, wear or damage appears. Sketch the route up and down before cutting materials, including where the cat lands and where a person can reach each joint for future inspection.
For product comparisons alongside this advice, see Ultimate PawHouse and Taj-MeowHall. The details below explain their sizes and uses.
Further reading: cats.org.uk; rspca.org.uk.
Ultimate PawHouse
Taj-MeowHall
Cat-Cave