A Bard (Lore) multiclassed with a level or so of Cleric (Knowledge) probably would work best.
I had once worked out a "Skill Monkey Build" that I think has some applicability here and could be adapted to this concept with some tweaking:
I am working on a Skill Monkey build, and I thought it might be nice to gather thoughts on both this build, and any other Skill Monkey builds people come up with.
Here is what I have so far:
Half-Elven Bard (Lore) / Cleric (Knowledge)
Half-Elf: +2 Charisma, +1 to two other abilities, Darkvision, Fey Ancestry, 2 Skill Proficiencies (any), Common and Elven and +1 Language Proficiency (any).
Background: Urchin (Slight of Hand Proficiency, Stealth Proficiency, Thieves Tools proficiency, Disguise Kit proficiency).
Bard 1: Armor: Light Armor; Weapons: Simple Weapons, Hand Crossbow, Longsword, Rapier, Short Sword; Instruments: 3 (any); Saves: Dex and Chr; Skills: 3 (any); Bardic Inspiration (d6); 2 Bard Cantrips; 4 known Bard spells; Spell Slots (full).
Bard 2: Jack of All Trades, Song of Rest (d6), +1 Bard spells known, spell slots.
Bard 3: Bard College: Lore; Cutting Words; Skill Expertise: 2 (any); Skill Proficiency: 3 (any); +1 Bard spells known, spell slots.
Bard 4: Ability Score Improvement/Feat; +1 Bard Cantrip; +1 Bard spells known, spell slots.
Cleric 1 (Knowledge): Armor Proficiency: Medium Armor, Shields; Skill Proficiency: 2 (of Arcana, History, Nature, Religion); Skill Expertise: 2 (of Arcana, History, Nature, Religion); Cleric Cantrips: 3; Cleric Spells Prepared: 1+Wis Bonus + Command + Identify; Ritual Casting; 2 Languages (any); Spell slots.
Cleric 2: Channel Divinity (Turn Undead) Channel Divinity (Knowledge of the Ages); +1 Cleric spells prepared; Spell Slots.
Skills Analysis: There are a total of 18 skills in the game. By 4th or 5th level, this PC is proficient in 12 of them (2 Half-Elf, 2 Background, 3 Bard, 3 (Bard Lore College), 2 (Cleric Divine Domain Knowledge)), with expertise in four of them (2 any, and 2 from a list of 4 from Cleric (Knowledge). For the remaining 6 skills you're not proficient in, you still add half your proficiency bonus to them instead of the full proficiency bonus (Jack of All Trades), and you can also expend a Channel Divinity use to become proficient in that skill for 10 minutes, once between every short rest. He also has the Guidance cantrip, which adds 1d4 to any ability check. The Bard spell Enhance Ability can also be used to grant advantage on one type of ability check.
Tool Proficiencies: Thieves Tools (open locks, disarm traps); Disguise Kit (prof bonus to disguise checks); Instruments (3).
AC: Medium Armor and Shield (Breastplate 14 AC, +2 Dex, +2 AC from Shield = 18 AC); various spells, like Shield of Faith, can improve this.
Languages: Common, Elven, +3 more (any)
Spell Slots: Full caster