The main FF series are a great series overall, my question to you is what platform do you own? If you are running a PC, you can easily have access to FFIII-X/X-2 (given you have a powerful enough pc for all of them), if you have a PS3, you can find most FF games in the PSone classics section with FF 1, FF 2, FF V, FF VI, FF VII, FF VIII, FF IX. If you have a PSP or a Vita you can even play FF III and FF IV if you get them from the store digitally or physically (FF III doesn't have a physical PSP copy here in the US though.)

If you own a PS2, definitely check out FFXII as well, open-world gameplay, and fascinating combat. My personal recommendation are around the FF V and FF VI games. If you want a unique experience, definitely play Final Fantasy V first, it has a job and ability system where you equip a job class on your character, and when you level up that job class, you learn an ability from that job class you can equip on any job class you choose to equip. It also has a fun, lighthearted story, and probably the funniest in the series with it's humor.

If you're more into the 3D FF's FFVII-XII are all great games, you can jump in at any order since they are independent from each other. That's about all I have to say on the subject, definitely let us know what interests you and we'll help you out!