What is the minimum/suggested sequence length for training an LSTM?
LSTMs would run into problems beyond 500 time steps. 
original paper by Hochreiter and Schmidhuber: "LSTM can learn to bridge minimal time lags in excess of 1000 discrete time steps."

Example: Your video is 60 seconds long. I would start by encoding 5 frames per second using a CNN (use resnet (SEnets have better performance but i havent read the paper) till the layer just before final affine layer which feeds into the softmax encode your images. Use these encodings as inputs in a GRU (Hence a 300 time steps for this GRU) and use its final state to make the class prediction (use a separate loss for each label?)