Orange Pi's are an alternative, but similar family of boards to the Raspberry Pi. Made in China they are gernerally cheaper and higher spec to the equivalent Raspberry Pi. The Orange Pi zero has built in Wifi and full sized USB port and Ethernet. There is no HDMI output, but you don't need it for the weather station and it saves on power.
My weather station and pywws software is now running on one of these Orange Pi zero.
At the time of writing this the Orange Pi Zero with 512Mb memory and quad core processor was $8.99 plus delivery. And if you wanted HDMI output, the Orange Pi One costs $9.99
The setup is almost identical to the Raspberry Pi except for the operating system. I used armbian for the Orange Pi Zero and have had no issues with it.
After that its just a matter of following the raspberry pi tutorial for setting up the pywws software.