Neural Network for predict a set in a certain time stamps
Since you have a transaction data set on your hands, we are talking clear-cut supervised learning here. And while you could certainly try to use neural networks, I think you should start simpler and switch to more complex and costly algorithms once you see the simple ones failing (this is generally a good idea).

Now form what you describe, you have some sort of time-series data, with a categorical quantity that you want to predict, for which you will want some sort of modified ARMA model. You could set up a logistic regression for each good you are interested in (i.e. beer, chocolate, potato, etc.) that will predict whether or not he will buy the product. The variables you feed into the model are a set of binary observations describing if he bought the product a day ago, a week ago, four weeks ago, etc.. Play around with those lags. The nice thing about logistic regression here is that you'll see right away what is the period of the purchases. If you see a large coefficient on the one-week-ago-variable, you know that he eats avocados weekly and so forth. Note that if something is purchased weekly, it's also purchased every four weeks, so you will have some correlation issues.

If you don't get decent predictions, you could try different models, e.g. trees or ensemble methods such as random forests or boosted trees. If those don't work either, you probably have a time series without clear periodicity. In that case you could try setting up your variables differently, e.g. using the number of days since he bought the product.

One last word of advice: You might want to check correlation between purchases. Maybe he buys avocados, tomato, and onion together to make delicious guacamole. If he then has some onions leftover, he might be inclined to buy more avocado and so on.