Connect to a local database via a wireless network in python

I'm creating a program in python that generates a bunch data and then stores it in a database. For testing purposes I'm using Sqlite as my database. However, I ultimately want to run this program on multiple machines and have them store the data in one central database. Sqlite says it's not good for having multiple clients connected to the central database. I use MySql pretty regularly so I could create a database using that or anything else you might recommend. All the machines including the machine hosting the database will be connected to a central network via a wireless router and will most likely be running Linux if that matters. However, if necessary I could could get a switch or something to connect the machines.

My question is using MySql or another database that you recommend, what is the python code to get the individual machines to connect to the central database?