Greetings.
Great that you have an instrument to practice on! Definately practicing on a digital piano is way more benefitial than practicing on a keyboard, especially that which has only 4 octaves.
Concerning exercises, be very wary of them as they have potential of injuring you. They are best suited to be played under teacher supervision, however, if you are cautious, you may receive benefit. The main culptit of damage from exercises, and a major one too, is that they tend to tense the hands. I do a ton of exercises, and my teacher always always stresses to me the importance of relaxation and staying relaxed whilst doing them. Not only the hands, but the face, legs, and arms. Every part of the body must remain calm and free.
Concerning specific exercises, I must recommend five finger exercises, scales, arpeggios, and Czerny. I am not a big advocate of Hanon, because I think that his exercises contain the same material that practicing other exercises, namely the five finger ones have. Crucial point again, is to never tense up. Look at some Czerny etudes. I don't remember the exact opus, but they are the short ones(about 8 measures in length), and stress a certain technique, such as scales for right hand, scales for left hand, trills, arpeggios, etc. Practice them thoroughly and carefully. Don't rush, never tense up. The aim is control and clearness of sound, not speed. Increase the tempo after gaining thorough control. I repeat a Czerny etudes many times and practice them in exercises, before playing the etudes in tempo. Tempo shouldn't be the number one goal. Control, freedom, and clarity should be thought of before tempo can be increased.
Topic: I have a new piano!