In short, yes, our keyboard and computer are enough, so long as you have some recording software! More detail follows:
There are two things coming out of that keyboard that you can record:
- The audio
- The MIDI data
Recording the audio will preserve the audio signal from the keyboard. Eventually, you'll need to do this if you want your recording to sound like your keyboard (as opposed to using some other sound source). To do this you'll need recording software of some kind. Audacity and Reaper are frequently mentioned for questions like this because they work well and don't cost anything to start out with (Reaper requires a license after 30 days). The resulting recording can be rendered to a wave file that will play in any audio player. You can encode it to MP3 afterwards if you like.
Recording the MIDI data will store exactly that: MIDI data, no audio signal. It's a set of instructions for telling some instrument what to play. If you play a MIDI file on your computer, what you're doing is sending those instructions to your soundcard. But you could also send those instructions right back to your keyboard, so the playback uses its sounds instead. Recording MIDI is great because you can edit the instructions before sending them back to the keyboard, but if you're a pianist and want to just play a piece straight through, you can probably skip this step and just go straight to audio. If you make a mistake performing that you want to fix in MIDI, it probably won't sound natural. Better to just re-record so you capture the human dynamics of playing.