if you want to get a feel for the series in general
>fe7
>fe8
>fe9

if you want to get a good feel for the newer games
>fe13
>fe14
>fe17

if you want a more unique experience
>fe4
>fe10 (beat fe9 first)
>fe15
>fe16

if you want a challenge
>fe5
>fe6
>fe11
>fe12

if you have nothing better to do
>fe1
>fe3

if you REALLY have nothing better to do
>fe2