Topics to learn in Neural Network
If you want to start with research, as you say, I would make sure not to skip the theory and underlying mathematics of machine learning. Knowing what model and hyperparameters to choose for a certain problem and being able to implement this quickly is very useful in corporate settings, but research mostly requires a deep mathematical understanding of what is going on.
In my opinion the book 'deep learning' by Goodfellow and Bengio has a good structure that allows you to get familiar with the mathematical foundations of deep learning. When you understand this, you will be able to read and understand state-of-the art papers if you want and do your own research. You can find the book for free online I think.