Hello everyone.
1. Mendelssohn G minor: Innovative, short and to the point, unlike many later romantic concertos, who seem to drag on forever, won't mention names but a two very notable concertos from the same composer ('connected' to Mendelssohn through Schumann...) spring to mind.
2. Schumann: Romantic at its best
3. Beethoven 4
4. Various Mozart concertos
5. Moszkowski: amazing, not just 'virtuoso-fare' or 'salon-music'

, superior to both Brahms concertos IMHO)
6. Rach 2
7. Mendelssohn D minor
8. Beethoven 5
9. Schubert-Liszt-Wanderer fantasy: because Schubert had to be on the list
10. Others I forgot / haven't heard (perhaps Weber no.1, but not Grieg, or Brahms...

)
Special mention to Mendelssohn's Violin concerto, probably even greater than the G minor. I didn't list most of later composers, because simply I don't really like their music, but, I'm open to suggestions for a 'gentle' introductory concerto.