Having played very little FF:

Retro/Classic: 1-6
Early 3D: 7-9
Modern: X, X-2, XIII Trilogy
MMO: XI, XIV

Star Wars/Xenoblade Lite: XII

You like VI and VII, so you could probably enjoy IV and IX as well!

Why do you dislike VIII and XIII

XIII for a lot of reasons, especially the characters, linearity didn't bother me

VIII was simply boring and i hated the changes made from VII for the background

I'll give IX a try first and let you know about it - i know it's high up there in most lists

1-3 are aged classics.

4-6 are the beginning of a great period.

7-9 are Final Fantasy at its peak.

10 onwards is where the series lost its way.

Good! I really hope you'll enjoy at least half as much as I did!

Timeless: 4, 6 & 9
Aged like a turd on a stick: 7, 8
Plays like a turd on a stick: X-2, 13, 13-2, lightning why did she return,
The i don't really care for: 1,2,5,X, 11,12 and 14

1-3,5 - Old Classics that I will probably never play
4-6 - The true classics
7-9 - Best balance between modern and classic
X, X2 - Technical stuff gets more important than the rest, but still great games
XII - Waiting for the HD remaster (someday) to finally play
XI, XIV - Why, why release it as a numbered series?
XIII, XIII-2, XIII-3 - The Shame

Also I like this:

The Good: IV, VI, VII, IX, X
The Bad: V, VIII, X-2
The Ugly: XIII, XIII-2, XIII-3
The unknown: I, II, III, XII