Square-Enix I want to start playing Final Fantasy.

Final Fantasy III and IV on the DS. Love both of them, both have very good stories and are fairly challenging.
As for the rest...you could check on the Wii Shop channel for Final Fantasy I (and maybe II), but it'll cost you Wii Points (800 I think, I could be wrong).
And IIRC V and VI are for the GameBoy Advance, though your best bet for finding those is used at your local game store. There's nothing wrong with used games though, I have I, II, IV, and VII: Dirge of Cerberus as used and all work perfectly.

EDIT: Apparently there is a GBA version of FFI and II as a compilation, I've never seen it though. It's called Final Fantasy I & II: Dawn of Souls.

 

Its actually quite easy to jump into Final Fantasy. Choose a main series game for a platform you have and go! At least, as long as its not Final Fantasy II or Final Fantasy VIII. To get specific, it shouldn't be too terribly hard to find copies of Final Fantasy IV for either GBA or DS (or just download the original English translation under Final Fantasy II on Virtual Console, though I'd go for the DS version, personally) as that's probably the best place to start since you really only have access to the first half of the series (if you had access to the PS1 games, I'd have said FFIX is the way to go.) Other than that, however, I'd recommend FFVI for the story (nothing against the Esper system, but it makes character diversity pointless), the GBA version of FFV for the job system and the hilarious script, FFIII for, again, the job system, though not as much for the story and FFI for showing where the series began as a surprisingly good unlicensed video game adaptation of Dungeons and Dragons. That said, the GBA version is the way I'd go for FFI, its easier, has a more coherent storyline and looks nicer than the NES version.

EDIT: Also, I always forget about this, but there are PC versions of FFVII and FFVIII, though I imagine that they're pretty tough to find now.

Availability breakdown of the whole main series:
Recommended for first time players:
FFI: NES, GBA (with FFII,) Virtual Console, PS1 (with FFI,) PSP (Great story for its time, but really just the best damn unlicensed video game adaptation of Dungeons and Dragons ever)
FFIII: DS (Relatively simple story, but expanded job system from the first game that lets you change jobs as you see fit)
FFIV: SNES (as FFII,) GBA, DS, Virtual Console (as FFII) (Epic storyline that is one of the best in the series, but job system has jobs locked to characters and, at least for the SNES/Virtual Console versions, you will be forced to use the party the game wants you to)
FFV: GBA, PS1 (with FFVI) (Somewhat boring story, but the GBA version's translation is quite possibly one of the funniest things you'll ever find in a video game, plus an expanded version of FFIII's job system)
FFVI: SNES (as FFIII,) GBA, PS1 (with FFV) (Great story, but the Esper system eliminates almost any real character diversity)
FFVII: PS1, PC, PSN (Overrated, but still has a great story, though the Materia system is even worse about eliminating character diversity than the Esper system)
FFIX: PS1, PSN (Arguably the best title in the whole series with arguably the best storyline, jobs are locked to the characters, but you're not forced to use a specific party this time around)

Not recommended for first time players:
FFII: GBA (with FFI,) PS1 (with FFI,) PSP (Not a bad storyline, but it has a horrible and completely broken leveling system)
FFVIII: PS1, PC, PSN (Awful storyline with less plot holes and more plot craters and the arbitrarily complex Junction system that has to be broken into pieces for it be any more than a pain in the ass)
FFX: PS2 (While it is a fan favorite, the story doesn't sit well with everyone, the battle system kicks ass, though)
FFXI: PS2, PC, XBox 360 (MMO, not even recommened in the realm of MMOs with stuff like World of Warcraft and DCU Online on the market)
FFXII: PS2 (Controversial due to the subtle storyline that was more political warfare in the background than epic quest in the foreground, plus the western RPG style battle system that a lot of people flat out hate)
FFXIII: PS3, XBox 360 (Controversial due to the ridiculously character driven narrative, the arguably overly simple battle system that almost plays itself and the fact that it is by far the most linear game in the series and that's saying something)
FFXIV: PC (MMO, probably the worst one on the market right now, too)

 

The PC versions are scattered all over the interweb ready for download, with their grpics patches and fixes and stuff. Noone buys those PC versions.

 

When I first played FF I've always felt that it can be overwelming since there are so many, including there spinoff series.

Anyway, I say start out with the Crystal Chronicals series since there exclusively for Nintendo systems (which you have listed). On the other hand, for the main series I'd start out with the GBA versions of 1 and 2, mainly because there fairly easy and will take at least 10-14 hours to finish.