Retrain or fine-tunning in Caffe a network with images of the existing categories

I'm quite new to caffe and this could be a non sense question.

I have trained my network from scrath. It trains well and gets a reasonable accuracy in tests. The question is about retraining or fine tunning this network. Suppose you have new samples of images of the same original categories and you want to teach the net with this new images (because for example the net fails to predict in this particular images).

As far a I know it is possible to resume training with a snapshot and solverstate or fine-tuning using only the weigths fo the training model. What is the best option in this case?. or is better to retrain the net with original images and new ones together?.

Think in a possible "incremental training" scheme, because not all the cases for a particular category are available in the initial training. Is it possible to retrain the net only with the new samples?. Should I change the learning rate or maintain any parameters in order to maintain the original accuracy in prediction when training with the new samples? the net should predict in original image set with the same behaviour arter fine tunning.

Thanks in advance.