I've spent a huge amount of time playing with similar stuff. The goal is to predict anything that you can make money on -- this can be obviously be price, but you can also try volatility, or predicting a probability distribution. Try relaxing constraints to find your signal: price ranges instead of exact prices, date ranges instead of exact dates. If you can output a probability, distribution, or confidence interval as well, that information can be used for position sizing (see Kelly criterion.)

If you start expanding beyond a small set of specific companies, don't forget to find data for delisted companies to avoid survivorship bias.