You need a way to input midi notes and signals. The good news is that virtually any digital keyboard will work for inputting MIDI notes, whether is costs $30 or thousands. If it has a MIDI port or a USB port, then it can transmit MIDI information. These days, USB has become the standard connection type for MIDI. 
There are other instruments that can input MIDI data, but keyboards are the main type. 
A midi controller is a device that is intended to send some kind of midi information, and it can be anything from a keyboard to a mixer to a small button pad. As I mentioned earlier, many kinds of information can be communicated over MIDI--in addition to note data and expression curves, you can send signals which can be assigned to keyboard shortcuts in your DAW, or assigned to knobs and sliders. 
Digital pianos come with their own sounds so they can be played independently of any computer setup. MIDI controllers don't usually come without any of their own sounds onboard, with the sole intention of being used to send midi data to your DAW and using those sounds. 
If you are a pianist, you will probably want a weighted-key option that feels close to the real thing. 
NOTE: velocity sensitive, semi-weighted, and fully weighted DO NOT MEAN THE SAME THING. If a certain kind of touch is very important to you as a pianist, go to a music store and try out different keyboards with different touches to see what you like. 
Digital Piano only Recommendation:

Yamaha P45 or P71 - Approx $400.
The Yamaha P series are quality and very durable. I've used my p120 almost daily for 13 years and it's still going strong. A couple of keys are beginning to stick. This is a legit digital piano, but has NO MOD WHEEL.
There are many kinds and makes of digital piano above this price range. Again, if you are a pianist and you want a specific feel and sound, the best thing to do is to try out different pianos in person. 
If you get a digital piano with no mod/pitch wheels, or programmable knobs and sliders, you may want to consider getting a device that is dedicated for that purpose. 
Controller only (Low Budget):

Behringer X-Touch Mini - Approx $50
Akai Professional MIDImix - Approx $100
About 12 years ago there were not as many cheap MIDI controller options, so after some experimenting I was able to rig up a gaming joystick as a midi controller, and it is what I have used ever since. Not bad for $15!
However, you may find that your best value for your money (especially if you do not want fully weighted keys) is one of the below options with keyboard and other wheels and sliders. 
Keyboard + Controller combinations (NON-WEIGHTED KEYS)

midiplus AKM320 MIDI Keyboard Controller - Approx $36
Nektar Impact LX49+ Keyboard Controller - Approx $160
Nektar Impact LX88 - Approx $320
Semi-weighted 88 key with modwheel and assignable controls.
Keyboard + Controller Combinations (WEIGHTED KEYS):

M-Audio Hammer 88 - Approx $400
Fully weighted hammer-style touch with MOD and PITCHBEND. 
Komplete Kontrol s88 Mk2 - Approx $1,040
Fully Weighted keys, assignable knobs, Native Instruments integration and free instruments. This seems like a pretty legit option.
ASSIGNMENT: look at options, do research, visit a music shop and try out options, especially if the touch is important to you as a pianist. 

How To Compose with MIDI and Virtual Instruments

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