First pass, using NodeMCU and sensor, powered via USB charger. Since a lot of the wireless technology is based on the ESP SOC this would be a good development platform to experiment with, so worth getting one to play with.
Solder (badly) the BME280 to a four core cable with a couple of two pin header connectors (GND, 3.3V) & (SCL, SDA) on the end. Connect to the pins on the NodeMCU (GND, 3.3V) & (D4, D5).
Install ESPEasy and configure it to have one BME280 device, connected using MQTT ultimately to OpenHAB. In the meantime tested connectivity by installing Mosquitto on my server. Named the ESP in the living room: “Lounge” and the BME280 sensor “Sensor”:
mosquitto_sub -v -t "/Lounge/Sensor/#" /Lounge/Sensor/status/LWT Connected /Lounge/Sensor/Temperature 16.24 /Lounge/Sensor/Humidity 54.18 /Lounge/Sensor/Pressure 1021.65
Too easy, but pretty ugly, with a USB charger hanging out of the wall socket.
Build two more using D1 mini boards, soldering the wires direct to the through hole vias. Deploy one as ‘BigShed’ and the other as ‘TopRoom’.