The Official Final Fantasy 1 FAQ - Because the front page is rather out of date!
1. What is the differences between all the versions? Which one should I play?
I'm not gonna get too specific, but this will give you a good idea:
NES/Famicom - Buggy, clunky, and has a choppy translation, but there's an old-school charm to it.
MSX - More colorful but the animation is worse, and is even buggier than the NES version. Not available in English.
WonderSwan Color (WSC) - 16-bit remake, some bugs corrected, a bunch of interface changes to make gamepay more smooth, and enemy stats buffed. Not available in English.
PlayStation (PS1) - Uses the WSC port as a base. Upgraded sound, difficulty modes, art gallery added in, and a redone translation. Part of the Final Fantasy Origins compilation.
GameBoy Advance (GBA) - Based off the PS1 port. Visuals and audio got downgraded, classes got rebalanced, all the bugs have been corrected, a whole slew of items have been added, and the magic system has been changed from charges to MP. All in all, this version is a lot easier, though there are some bonus dungeons that compensate for the main story's lower difficulty. Translation again redone to be more in line with the modern FF games. Part of the Final Fantasy I & II: Dawn of Souls compilation.
PSP - Based off the GBA port. The audios and visuals got upgraded again, and the game has never looked or sounded any better. Another hard bonus dungeon has been added in, and has a hilarious glitch that lets you equip any weapon/armor to any class, but is otherwise the same as the GBA version.
Pixel Remaster - Based off the GBA port, with the audio/visuals once again being redone. But some stuff has been removed, such as the bonus dungeons and some of the new items. The older, charge-based magic system also returns.
Personally, I prefer Origins out of all them, as the lack of Ethers makes for a game more focused around resource-management, but go with whatever sounds best to you.
2. How do I open up the map?
In the NES/GBA version, hold the B button and press Select. In the PS1 version, hold down the O button and press Select. In the PSP version, hold down the O button and press Start. The NES version just shows one big map, while the other ports let you zoom in, and see where which location is. However, you can only see areas that you've already entered.
3. What is the Class Change Quest? How does it work?
The Class Change Quest (or as I prefer to call it, Class Promotion) is a side quest which many players choose to do. What you get from promotion depends on the character and version you're playing. In the pre-GBA versions, promotion just expands your equipment and magic selection.
But for the GBA version and onwards, your stat growths are also boosted. If you're a perfectionist, you want to promote as early as possible to maximize stats. This can either be done through a) only killing bosses and running from everything else until class change or b) have a Red Mage and kill off the rest of your party, and use only the Red Mage until you promote, since promotion doesn't affect their stat growths. This is overkill though, and is just for people who like seeing high numbers. You'll be fine promoting whenever you feel like it.
4. What are the playable characters in this game?
There are 6. They are: Fighter/Warrior, Black Belt/Monk, Thief, Black Mage, White Mage, and Red Mage. I assume that anyone reading this already knows what White Magic and Black Magic are, but if you don't: White Magic is healing and undead killing magic, while Black Magic is damaging elemental magic like Fire, Blizzard, etc. Buffs, debuffs, and status effects are split up between the two colors.
As said earlier, the GBA version rebalances the classes, which all future remakes carry over, but for brevity's sake I'll just say "GBA FF1."
Fighter - The Fighter has all-around high stats, and a better equipment selection than any other starting class. On the downside, they have no magic. They promote to Knight which lets them equip almost anything and cast low-level White Magic. The Fighter is called "Warrior" in later editions. They're by far the best party member, and carrying no Fighters is an easy way to make the game harder.
Black Belt - The Black Belt can't equip much, as they're supposed to go without equipment and fight naked. On paper, they're a glass cannon. In practice, they want to use weapons until lv7, and they won't outdamage a properly-equipped Fighter/Knight until lv21. They become a Master after promotion, which only changes one thing: their magic defense growth gets worse.
In the MSX version, the Black Belt doesn't have their unique unarmed stats, rendering them useless.
In GBA FF1, they're called "Monk." Their unarmed stats are higher, and don't ever need to use weapons. They'll take the title of "best damage dealer" quick, and will have the highest HP too.
Thief - The Thief only has two good stats: Luck and Agility. Neither are useful. It's commonly stated that the Thief has a higher chance of running away, but in the NES version, that's bugged to where that's not the case. When they promote, they become a Ninja, which is essentially a slightly worse Knight that gains low-level Black Magic instead of White Magic.
In GBA FF1, they can deal damage on par with a Warrior, and the Ninja is still just a Knight but with Black Magic.
Black Mage - The Black Mage can use most Black Magic spells, but in return, all their stats (except for Intelligence) are terrible. Intelligence is supposed to determine how effective your spells are, but in the old versions, Intelligence is bugged and does nothing. The limited magic system makes it so that you can only cast a scant few spells in a dungeon before having to retreat and heal at a town. That being said, those few spells are useful when you need them, so they're not all bad. They promote to a Black Wizard, letting them use all Black Magic spells.
In GBA FF1, Intelligence works, meaning the Black Mage's spells are the most effective out of anyone. In addition, the modernized magic system and addition of Ethers allows the Black Mage to use their spells far more often. As long as you have the gil to shell out for Ethers, you can keep spamming your magic.
White Mage - The White Mage uses most White Magic spells, and doesn't have any good stats barring Intelligence, putting them in the same boat as the Black Mage. They promote to a White Wizard, granting them all White Magic spells.
Like with the Black Mage, GBA FF1's overall changes makes the White Mage more useful, and their exclusive healing spells makes the bonus dungeons more manageable.
Red Mage - The Red Mage is a jack of all trades; they can use decent equipment, and some black and white magic. They start off as the best character, but as the game goes on, they get weaker due to less options being available. Still, the hardest parts of the game are early on, so they'll definitely pull their weight when they're most needed. After promoting into a Red Wizard, they get more spells and equipment.
In GBA FF1, the Red Wizard is the only promotion to not have boosted stat growths.
5. What is this 15 Puzzle Slider?
While you're in the Ship button, hold the confirm button and press the back/cancel button 55 times. Completing it will get you 100 gil. In the WSC/PS1 versions, completing it will get you 2000-10000 gil depending on how fast you do it. In the GBA/GBA/PSP remakes, you'll either get useful items like Blue Curtains, or crappy items like Echo Grasses, again depending on how fast you complete it. The Pixel Remaster doesn't give anything for completing it.
6. Is the White Mage a man or a woman?
Yes.
7. I'm trapped at the Soul of Chaos dungeons! Everyone's at 1 HP and 0 MP and I have no recovery items! What do I do!?
If you die in the Soul of Chaos dungeons, then you'll just teleport out to the entrance with 1HP and 0MP.
8. Do any of the spells stack?
Additive buffs (such as TMPR/Steel/Temper) will stack, up until that particular stat hits a cap. Multiplicative buffs, such as FAST/Haste or the A/Nul spells don't stack. This is true even if you're wearing armor that already applies the buff, such as how the Ribbon halves all magical damage.
9. What's the best party?
That's different depending on the version, and what you mean by the "best". If by "best" you mean most powerful at the highest level, then that'd be four Masters, since they can deal the most damage against anything in one turn. Of course, good luck getting to that level with them to begin with!
If by best you mean "quickest to clear the game with", then the question is a lot easier to answer. Empirically speaking, the fastest recorded speedruns have been done with:
Fighter/Fighter/Fighter/Red Mage
Fighter/Fighter/Red Mage/Red Mage
Fighter/Fighter/Red Mage/White Mage
There hasn't been as much experimentation or discussion over the MSX/WSC/PS1 versions, but mechanically they're pretty similar, so those parties should still work pretty well over there. For GBA FF1 versions, despite lots of discussion I haven't really noticed much of a consensus, probably because the classes are all so balanced. I would say if you do the bonus dungeons, bring a White Wizard.
10. How can I get gil easier?
Go to the Finger Point, which is that finger-looking area of land northeast of Pravoka. It has monsters stronger than what you're normally supposed to fight. If you're playing the NES version, and you're too underleveled for the finger point, you can go to an Inn, reset the game, go into the sea, fight Kyozus, go back into the Inn, repeat. In the WSC/PS1 versions, just play the ship game a couple of times.