Dark Souls doesn't have classes in the most usual sense (i.e. one that locks you to a certain skill trees like in, for example, Dragon Age), but the character type you pick when you begin the game will weight your starting stats in a certain direction, and give you equipment that sets you up a little better for different styles of play. As you progress through the game you can develop your character in different directions, and, with different equipment, can create a unique, fine tuned character.
All classes have access to Battle Arts, unique skills which differ depending on the weapon you're using – it could be a devastating attack, or a damage buff. Battle Arts draw from your focus (your magic), rather than stamina, even if your character isn't a spellcaster.
The stats for Dark Souls 3 are similar to Dark Souls 2, although there's no Adaptability, and we have, instead, Luck. The levelling and character menus will look familiar if you've played any souls games before, but if you haven't they can seem complicated at first glance. They're not really that bad.
Vigor – mostly governs your hit points, but also raises your frost resistance, for some reason (which is actually more important than you'd think given that a lot of the bosses have a frosty element to them).
Attunement – governs your focus points (which is functionally the same as your mana) and you attunement slots, which are what limit the number of spells you can carry. You can think of them as spell slots, if you're more familiar with western RPGs.
Endurance – endurance governs stamina, which restricts how far you can sprint and how many swings you can take with your weapon before you get knackered out. Endurance also increases your resistance to lightning and bleeding damage.
Vitality – increases your max equipment load, resistance to physical damage, and resistance to poison.
Strength – allows you to wield heavy weapons and armour, as well as increasing the damage you do with strength based weapons (like greatswords) and your resistance to fire damage.
Dexterity – dexterity is required to wield advanced weapons. It also reduces your spellcasting time, and the damage you receive from falling.
Intelligence – this increases your magic defence, but you also need it for casting sorcery and pyromancy based spells.
Faith – Faith is required for casting miracles and pyromancies (you'll note that pyromancy needs both Faith and Intelligence). Also increases your dark defence.
Luck – Luck increases your bleeding and poison capabilities, and your resistance to curses. It also makes it likely for your enemies to drop more items on death, which can be very useful given how much equipment can increase your capabilities in the game.
At the start of Dark Souls 3, and with a cheeriness inherent to Souls games, your character leaves their grave, and can take a Burial Gift with them, functioning the same as the starting gifts from Dark Souls and Dark Souls 2. You can also choose to start with no gift, presumably because nobody cared enough to bury you with one. These item descriptions are taken directly from the game.
None – No sign of a burial gift or otherwise.
Black Firebomb – Firebomb charged with a special black powder. An uncouth gift for the departed.
Fire Gem – Material used to upgrade to fire weapons. More appropriate for a warrior than pretty trinkets.
Sovereignless Soul – The sovereignless soul of one who slept beside you. Use to acquire many souls.
Rusted Gold Coin – Burial item for good fortune after death. Greatly increases item discovery for a short while.
Cracked Red Eye Orb – Online play item. Once use only. Become a dark spirit and invade another world.
Young White Branch – Branch of a young white birch, perhaps an offering of peace. Can be used to blend into environment, but only once.
"An obscure knight of poor renown who collapsed roaming the land. Sturdy, owing to high vitality and stout armor." The Knight is chosen by a lot of people for their first run through of the game, because this class balances being able to take a hit and deal a hit pretty well.
"A mercenary and veteran of the battlefield. High dexterity allows masterful wielding of dual scimitars." The merc is much faster than the knight, but the trade off is in the strength and vitality, so you'd better use that speed to keep moving.
"Decendant of northern warriors famed for their brawn. Utilizes high strength to wield a heavy battleaxe." Warriors are incredibly strong, but have comparatively low dexterity and vitality. The idea is to hit something hard enough that it can't get up to hit you back. Warriors are also, not to put too fine a point on it, quite stupid, so there's no point trying to teach them any spells.
"A former herald who journeyed to finish a quest undertaken. Wields a sturdy spear and employs a gentle restorative miracle." As you can see from the stats, heralds are a very even class, so you can choose to focus on almost any combat path from starting as one. Heralds use magic from the school of miracles, which is more focused on passive magic like healing than it is on damage.
Spear; kite shield; full suit of herald armour; talisman (spellcasting weapon). The herald also starts with the miracle spell Heal.
"A common thief and pitiful deserter. Wields a dagger intended for backstabs alongside a military-issue bow." As the description suggests, thieves rely mostly on their wits in battle – which in this case means your wits. Daggers have high critical hit damage, which is why they're so good for backstabs, but that depends on you getting behind the enemy in the first place. The high luck that thieves have does mean that they'll get better equipment earlier on in the game, however.
"An assassin who stalks their prey from the shadows. Favors sorceries in addition to thrusting swords." The assassin doesn't have great vitality or strength, but combines high dexterity with high attunement and a good starting intelligence, meaning you can eventually build a good roster of spells alongside fast combat. The assassin uses sorcery, which is a varied type of magic, and the starting spell masks your noise so you can sneak past enemies if you can't be arsed.
Estoc; target shield; full suit of assassin armour; sorcerer's staff (spellcasting weapon). The assassin also starts with the sorcery spell Spook.
"A loner who left formal academia to pursue further research. Commands soul sorceries using high intelligence." The sorcerer is your classic squishy spellcaster type. High intelligence and lots of spell slots, but will go down in a couple of hits, so be careful.
Mail breaker; leather shield; full sorcerer's robes set; sorcerer's staff (spellcasting weapon); Young Dragon Ring (boosts power of sorceries). The sorcerer also starts with the spells Soul Arrow and Heavy Soul Arrow.
"A pyromancer from a remote region who manipulates flame. Also an adept close combat warrior who wields a hand axe." The pyromancer is a damage spellcaster type, so combines a damage dealing school of magic with higher strength and vigor than other spellcaster types, meaning you can wallop enemies a good'un if you want.
Hand axe; caduceus round shield; full pyromancer's garb set; pyromancy flame (spellcasting weapon); great swamp ring (boosts pyromancy spells). The pyromancer also starts with the pyromancy spell fireball.
"A traveling cleric who collapsed from exhaustion. Channels high faith to cast many and varied miracles." The cleric is a magically amped kind of herald, so has higher spellcasting abilities in exchange for slightly lower physical combat ones. The cleric starts with two miracle spells instead of one, including Force, which can stagger enemies away from you if you need a bit of breathing space.
Mace; blue wooden shield; full cleric robes set; cleric's sacred chime (spellcasting weapon). Clerics also start with the sorcery spells Heal and Force.
"Naked and of unknown origin. Either an unimaginable fool in life, or was stripped of possessions upon burial." This is the starting class if you want a bit more of a challenge. The deprived isn't especially good at anything, and you wake in your grave with nothing. But, on the other hand, they aren't especially bad at anything either. They're just an average person.
Cub; plank shield. Rack all else. No armour. Just a tasteful loincloth. Pants Man.