To record MIDI as MP3 in Reaper:
Add two tracks.
Input: MIDI > Select MIDI keyboard
FX > Select Synth VST
Recording monitoring: ON (Speaker symbol)
Press Track 1 recording button so it starts writing when you record.
Open instrument window (press FX button)
You can now play your Synth and record MIDI.
When you playback the recording you will notice any adjustments you make inside the Synth are not recorded; only the MIDI keyboard keystrokes are recorded.
To record the actual audio as wave form:
IN button: Record output (multichannel, latency compensated).
Press Track 2 recording button so it starts writing when you record.
You can again start recording and now track 2 will contain the audio as wave form.
When you are happy with the result, go to File > Render… to generate project as an MP3 file.