You should break your problem down into simple parts, which it seems you are on-track to do. Your ultimate goal appears to break down into the following sub-tasks (not in order):
- Read sensor value
- Connect to a WiFi network
- Connect to a MySQL server
- Send sensor data to MySQL database
You are unlikely to find a single library to do all of these tasks, but as progress in solving each step, any library that works is the "Right" one, in general. Choose a library that solves an individual task.
You say you tried to upload a simple program to only connect to WiFi, but that it did not compile. The clue to why it did not compile will be found in the actual compile error message. If you can update your question with the error message and the code to the simple program, you can get some guidance from the users of this site to solve that problem.