Using different timesteps for training data and target value
is it ok to use daily prices?


You can use the daily prices as time series to forecast an arbitrary horizon.


  LSTM vs NN


In short, vanilla NN have no memory of previous inputs whereas LSTM NN have. This is particularly useful in your problem because LSTM can learn the temporal (sequential) characteristics of your dataset and therefore forecast several steps ahead. LSTM RNN can learn the dynamics of your problem (vanilla NN cannot). A useful Python/Keras tutorial for your problem can be found here.


  Regression vs Classification


In short, classification is the problem of discriminating a sample into discrete categories. Regression refers to using past values of a signal (or more) to estimate future values of the same (or other) signals. In your case, regression is what you ask for.