After learning the basic major and minor chords, it is a good idea to start connecting them in the classical manner. This means chord progressions where each successive chord contains at least one note from the previous chord. There are of course many exceptions to this in the literature, but it is the basic way of moving from one chord to the next. A good harmony book will be of use at this point.
The next thing I would do, if I were you, would be to learn all inversions of chords, the 6 and 6/4 chords. These are variations on major and minor chords that give different sounds and that can open up your playing and voice leading.
I also second learning seventh chords. Pay special attention to the seventh chord on the dominant (fifth degree of the key), as it is quite important.
Diminished and augmented chords can be a way to spice up your harmony, to make it more interesting, to add tension. You may want to consult a book on harmony on ways to prepare and resolve dissonances caused by the tritone on diminished chords (a diminished chord is two minor thirds). For classical music, this is essential, but for more modern music dissonances are not given special treatment. Augmented chords (two major thirds) are not a part of the natural scales, but the third degree (while ascending) of minor melodic scales is augmented.
Another thing is to distribute chords between your hands, to give them more space, as if a chorus is singing them. Experiment with open spacing and closed spacing. This is really helpful for composition, where not every piece consists of chords played by one hand and a melody in the other hand--at times you want a melodic bass, or an interesting tenor or alto line, and thinking of chords spread out between the hands can facilitate this.
In short, as a beginner I would first learn the major and minor chords, their inversions, then seventh chords, and then diminished and augmented chords. There are, of course, many more types of chords. Getting a good harmony text will help you learn these. It is also a good idea to start analyzing the harmony of works of musical art that you like--what harmonies, what progressions did the composer use?