Marry - FFVII, FFVI, FFIV, FFIX, FFV (in that order)
One Night Stand - FFIII (DS), FFX, FFVIII, FFXII, and FFXI only if you like MMO
Carcus - FFI, FFII, FFXIII (may want to play FFI since it started it all and is actually pretty good, but my guess is a new player would not be able to 'get' the old school gameplay)

The SNES and PS1 games are where it's at, so I would tell my friend to start with those, but leave V and VIII for last. V because I feel it has a bigger learning curve than the other games from that era, and VIII because it's not as good and I want my friend to understand how great this series is before he/she tries the 'other' entries.