Artificer: gives Arcana, History, Investigation, Medicine, Nature, Perception, &Sleight of Hand
- Sage gives History, & one of Arcana or Religion So any four skills
- Guild Artisan gives Persuasion, & one of Insight or History. So Persuasion, one from artificer, & any two
- Noble gives History, & one of Animal Handling or Persuasion. So one artificer skill, one of animal handling or persuade, & any two.
- Sage gives History, and one of Arcana or Religion. So any four skills
- Hermit gives Religion, and one of Survival or Medicine. So any four skills.
- Folk Hero gives Survival, and one of Animal Handling or Nature. So one from artificer, survival, & any two.
- Sailor gives Athletics, and one of Acrobatics or Perception. So one artificer, athletics, & any two skills
- Charlatan gives Deception, and either Sleight of Hand or Insight. So deception & one artificer pus any two.
- Urchin gives Sleight of Hand, and one of Deception or Stealth. So Sleight of hand, one artificer, plus any two
Barbarian: 2 from animal handling, athletics, intimidation, nature, perception, & survival
- Nomad gives Survival skill, and your choice of either Animal Handling, Medicine, Nature, or Perception... So any four skills
- Folk Hero gives Survival, and one of Animal Handling or Nature. So any four skills
- Noble gives History, and one of Animal Handling or Persuasion. So History, one from the barbarian list, and any two other skills.
- Soldier Athletics, and one of Animal Handling or Intimidation. So any four skills
- Outlander gives Survival, and one of Athletics or Intimidation. So any four skills
- Sailor gives Athletics, and one of Acrobatics or Perception. So any four skills
- Criminal gives Stealth, and either Deception or Intimidation. So Stealth, 1 from the barbarian list, & any two.
- Hermit gives Religion, and one of Survival or Medicine. So religion, from barbarian, & any two.
Bard: Any 3
- Depending on your reading, this actually works against the bard because even though it's the only class with any skill options at first it doesn't get the same skill from a background as a result so is limited to the background's skills as offered.
Cleric: Two from history, insight, medicine, persuasion, & religion
- Noble gives History, and one of Animal Handling or Persuasion. So any four.
- Sage gives History, and one of Arcana or Religion. So any four
- Hermit gives Religion, and one of Survival or Medicine. So any four.
- Acloyte gives Religion, and either Insight or Persuasion. So one cleric, religion, & any two.
- Entertainer gives Performance, and one of Acrobatics or Persuasion. So one cleric, performance, & any two
- Guild Artisan gives Persuasion, & one of Insight or History. So any four.
Druid: Two from Arcana, Animal handling, insight, medicine, nature, perception, religion, & survival
- Sage gives History, and one of Arcana or Religion. So any four
- Nomad gives Survival skill, and your choice of either Animal Handling, Medicine, Nature, or Perception... So any four skills
- Folk Hero gives Survival, and one of Animal Handling or Nature. So any four skills
- Noble gives History, and one of Animal Handling or Persuasion. So History, one from the Druid list, and any two other skills.
- Soldier Athletics, and one of Animal Handling or Intimidation. So any four skills
- Hermit gives Religion, and one of Survival or Medicine. So any four.
- I'm tired of showing that more backgrounds give access to any skill choices than not
Fighter: Two from Acrobatics, Animal Handling, Athletics, History, Insight, Intimidation, Perception, & Survival
Monk: Two from Acrobatics, Athletics, History, Insight, Religion, and Stealth
Paladin: Athletics, Insight, Intimidation, Medicine, Persuasion, & Religion
Ranger: Three from Animal Handling,Athletics, Insight, Investigation, Nature, Perception, Stealth, & Survival
Rogue: Four from Acrobatics, Athletics, Deception. Insight, Intimidation, Investigation, Perception, Performance. Persuasion, Sleight of Hand, & Stealth
- You mentioned rogue sage though so I'll fill this in...
- Outlander gives Survival, and one of Athletics or Intimidation. So three rogue, survival, & any two skills
- Sailor gives Athletics, and one of Acrobatics or Perception. So any six skills
- Soldier Athletics, and one of Animal Handling or Intimidation. So any six skills
- Entertainer gives Performance, and one of Acrobatics or Persuasion. So any six.
- Charlatan gives Deception, and either Sleight of Hand or Insight. So any six.
- Criminal gives Stealth, and either Deception or Intimidation. So any six.
- Urchin gives Sleight of Hand, and one of Deception or Stealth. So any Six.
- Entertainer gives Performance, and one of Acrobatics or Persuasion. So any six
- Guild Artisan gives Persuasion, & one of Insight or History. So any six.
- Noble gives History, and one of Animal Handling or Persuasion. So any six.
- Acloyte gives Religion, and either Insight or Persuasion. So three rogue, history, & any two.
- Sage: gives History, and one of Arcana or Religion. So four from rogue, history, & either arcana or religion.
Sorcerer: Two from Arcana, Deception, Insight, Intimidation, Persuasion, & Religion
Warlock: Two from Arcana,Deception, History, Intimidation, Investigation, Nature, & Religion
Wizard: Two from Arcana, History, Insight, Investigation, Medicine, & Religion