Geiger - Muller tube will detect x-rays. Many designs for the low-current high voltage power supply can be found online. Old Soviet G-M tubes can be gotten at reasonable prices.
PIN photodiodes do not require high voltages but the extremely low current signal output makes them subject to noise pickup unless well shielded.
Scintillation crystal + photomultiplier detectors are the most linear, quite sensitive, and can be very efficient, but are more costly and also require high voltage.
Overall I would recommend the G-M tube approach.