as far as I know, there's actually quite a few FF series that has sequel or prequel. Some of the FF Games that has sequels are :
FINAL FANTASY TACTICS Series
1. FF Tactics (PS)
2. FF Tactics : War of the Lions (PSP)
3. FF Tactics Advance (GBA)
4. FF Tactics A2 (NDS)
FFT:WOTL is actually a remake of FFT. Therefore, the story would be very very similar with some addition here and there. Since you don't have PSP, i think you can play FFT with emulator on PC. Try the FFT, it was one of the best game i have ever played in my life. About FFTA & FFTA2, although they are in the same series, there's no link between the story. So you can play in any order.
FINAL FANTASY X Series
1. FF X (PS2)
2. FF X-2 (PS2)
If you'd like to, try emulator, and play from FF X first.
FINAL FANTASY VII Series
1. FF7 : Before Crisis (Cellphone)
2. FF7 : Crisis Core (PSP)
3. FF7 (PS)
4. Dirge of Cerberus (PS2)
FF7 is one of the best RPG at Playstation console. Heck, maybe one of the best ever created in the world. I suggest you to at least try it (with emulator, if you don’t want to afford a new PS Console). And it’s not a must to play the prequels to be able to fully enjoy the game.
All of FF games in NDS (FF3, FF4, FF Crystal Chronicle, etc) can be played in any order since there's no relation between the stories.