What ML algorithm can I use for building a "recommended" list for players? We have a large touchscreen kiosk in local malls where people can go up to it and play a game under different categories. We want to implement ML to build a recommended list of games for each player. For now, let's assume there are 5 different games under each of the 4 categories and the games can be either available or unavailable at any given time. Also, there is a table containing a log of each play and a table of all the games.

Ideally, we would want to pass 2 different data sets; example: a list of all the plays in the last 30 days with any necessary data, and a list of all the currently available games to play with the necessary "relatable" data. Out of this, we would then end up with a list of the top 10 recommended games for each player based on all that data. There will be more data than just the game's category to tie it together to the player/person, but I want to get a simple demo working first.

I am guessing I need to look into some type of recommendation system but I'm not sure which would best to try out. For now, we are looking at using Python; AWS's ML tool will be too costly. I am open to recommendations on other languages/tools.
Before jumping into machine learning solutions, it would be good to think more about the problem you're solving. If there are only 20 games and some are unavailable at any given time, then a well laid-out menu with good navigation is superior to a recommender system. Recommender systems are only appropriate when people cannot adequately parse all of the available options.

If you do want personalized recommendations, you don't even have to start with machine learning models. You can simply recommend that players keep playing the same games or the most popular games.

And if it turns out that machine learned models are best, I suggest looking at association rule mining based on unary data (which gives you shopping-basket recommendations: people who played games A, B, and C also played games D and E) or some variety of collaborative filtering based on ratings data (which gives you a user-item preference space). That totally depends on what sort of feedback you get from users about their individual game experiences.