This is not rocket science: dipole and ground plane are the most basic antennas you can build. And they can be good performers too! Here is a picture of the 1090 MHz GP I assembled for my ADS-B reception tests.
It is built around a panel-mount BNC socket. Each of the three solid copper wires is about 6.6 cm long and there is a 10 kohm 1/4W carbon resistor across "hot" and "cold" points to discharge static electricity right at the source.
This GP performs equally well with and without resistor, so leave it in place. This antenna is omnidirectional, and depending on its horizon it can bring up signals as far as 100 km away (E4000 tuner, airplane above 10'000 m). In this screenshot my receiver is below the ISSxyz airplane: