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Best way to get started making multiplayer games

I like programming in Python and I’ve spend some time using Corona SDK. I’m looking for the best way to get started with making multiplayer games. And, I want to make the games available to my students who tend to use their phones more than desktop computers. So, I’d like the game to be web based- like Kahoot! for example. But I am open to developing mobile games for iOS and Android- most of my students have iOS, I have an Android phone. Is it worthwhile to do game development in Python? Unity seems like it’s a great way to go except for cost ($25 per month is a bit more than I’d like to spend to get started. Even so, I’m open to all opinions. Thanks in advance!