Most of the tips below have been written down during the Wallis Days '98 and were told by Ken Wallis during a visit to his collection of autogyros.
Fuselage
Don't make the fuselage too stable for banking. Both stable and instable fuselages are sensitive to gusts. The ideal fuselage is just stable with respect to it's angle of attack. The stability of the fuselage can be tested with a simple scale model.
Tailplanes
Mount the horizontal tailplanes in the slipstream of your propeller. It makes them more effective. The effectiveness increases with an amount of Δvp/v, in which v is the flying speed and Δvp is the increase in airspeed over the tailplanes due to the propeller.
Systems
Beware that a pusher propeller is both carnivorous and coming in your direction when you start your engine. If you use an electric starter, you are safe in your autogyro. But an electric starter is heavy and if it fails, you will still have to start your engine by hand.
If you start your propeller by hand, it is nice to have one hand on the airframe. When the thrust is more than expected, you can push the autogyroback with that same hand. A "dead-man" switch (a switch that only makes contact as long as you are pushing it down) mounted on the place where you should hold the pushing hand will allow you to shut down your engine if something is really wrong with it. When the engine is running fine you can use the real on-switch and let go of the dead-man switch.
Apart from using a freewheel on the rotor drive, use a "spring back" rotor clutch handle that disengages when you open the throttle.
A "Fixed-wing" type of throttle is more in conformation with its use than a "helicopter" type. Some fixed-wing aircraft use a so-called "safety-throttle". This is a throttle that tends to go to full gas instead of going to idle when the rod or cable breaks. In flight, this is safer, because in case of a broken cable or rod you do not need to make an emergency landing. Landing and maintaining height is done by switching the engine on and off in such a situation. This construction will surely not improve safety when doing a hand-start.
A small ball-compass is about the lightest compass you can use.
If you are doing night flights: light the wool thuft!
Cross cables on parts that suffer from severe vibration.
A high and narrow windscreen does not take away to much of the view if it is wet.
force the stick to steer to the side of the advancing blade during spin-up. Both the engine and the rotor give a torque during spin-up.
Use a rotortachometer.
Two trimhandles are sufficient: one for each conrlol rod. If you mount then next to each other, they can be operated in one movement.
during engine start and rotor pre-rotation, the stick can be locked in the foremost position.
Undercarriage
use (parking-) breakes on all wheels.
design the undercarriage in such a way that you will not be tackled when hand-starting the engine.
When the autogyro has an enclosed cockpit, make it clear whether the rudder is controlled by pedals or by a bar. A bar is used more often, and is therefore what people expect.
Make the undercarriage steer the same way as the rudder. It is unnatural, but als even Sikorsky did not have the heart to change the direction of the rudder control.
It is nice to have the center of gravity of the whole aircraft close to the main wheels. This could mean that the nose wheel does not touch the ground when the pilot is not on board. This is not a problem and in fact quite common.
Rotor
use teeter stops to avoid "sailing" of the blades during low rotor rpm.
Have the rotor torque work against the engine torque during take-off.
If you want to spin up the rotor by hand, There is a preferred direction of rotation: right blade forward, unless you are designing the aircraft for left-handed pilots.
Ground material
If a blade strut counteracts the rotation of the rotor, mark it with "Fit first, remove last".