If new, below is a breakdown of DnD vocabulary regarding classes and a list of choices possible. If you have played before, the standard 13* classes are playable. Yes - artificer - No Blood Hunter
Your character's class is simply a mechanical way to categorize them, thus providing a path for them to become stronger in a game balance sort of way. Your character is still your character, don't feel beholden to have to match your class to your race, or abilities, or even party makeup. Pick the path(class) you think fits best for the story you want to tell. In the Player's Handbook, you have the choices outlined below. Some vocabulary for you:
Support
are known to heal allies' wounds, weaken enemies with magical effects, or strengthen allies with magic.
Melee Attackers
are built to deal damage with weapons like swords, daggers, axes, and warhammers.
Ranged Attackers
can use crossbows, bows, and thrown weapons to great effect.
Spellcasters
have access to spells. They each have a spell list, which includes all spells that can be learned(known) and prepared (to be used that in-game day) by a character with that class. As spellcasters level up, they gain access to more and higher-level spell slots, which are used up when a spell is cast. Many Spellcasters have access to Cantrips, which don't "use up" any spell slots when they're cast.
Full-Casters: High number of spells available to use each game day, plus access to higher-level spells.
Half-Casters: Low number of spells available to use each game day, and the power level of those spells is lower than Full-Casters.
Divine Spellcasters (Clerics, Paladins, Druids): Choose which spells you prepare each day from your entire Spell List.
Arcane Spellcasters (Bards, Rangers, Sorcerers, Warlocks, Wizards*): The list of Known spells and Prepared spells are the same for these classes(except for Wizards), as they can only gain/replace their known spells upon leveling up.
*Wizards: "Arcane" Full-Casters who prepare spells each day.
Number of Known Spells: increases when leveling up and finding Spellbooks/Scrolls in the world, they can copy into their spellbooks.
Prepared Spells: Wizards must choose to prepare spells each day from the list of spells they know (memorize).