If you decide on multiclassing to gain Expertise, there are two ways to acquire it: Rogue 1 and Bard 3. I'll list some of the pros and come of each.
Rogue
Pros: Only takes 1 level to acquire Expertise. Gain +1d6 Sneak Attack and one skill proficiency. Going to Rogue 2 grants Cunning Action. Multiclass prerequisite ability score is Dex 13, which you already have. Going to Rogue 3 ups Sneak Attack to +2d6 and grants a subclass (Thief/Assassin/Mastermind are all good choices)
Cons: No spell slot progression unless taken to Rogue 3 for Arcane Trickster, and even then it's slower than your Ranger spell slot progression. Thieves Tools proficiency is wasted, as you already have two Rogues who can get advantage by using the Help action. Party Rogues may feel that you're stepping on toes.
Bard
Pros: Faster spell slot progression than Ranger. Gain access to useful cantrips like Message, Mage Hand, Prestidigitation, and Minor Illusion. Jack of All Trades boosts your nonproficient skills and initiative rolls. Bardic Inspiration and Song of Healing add a measure of support. Both Bard Colleges have useful 3rd level abilities (Cutting Words/Combat Inspiration). Lore Bard grants extra skill proficiencies on top of the one gained by going Bard.
Cons: Takes three levels to acquire Expertise. Multiclass prerequisite ability score is Cha 13. Bardic Inspiration uses and Bard spells use Cha. Valor Bard gained proficiencies are wasted. Musical instrument proficiency is mostly useless, as you're already using a component pouch for Ranger spells.
If you decide to multiclass, then I would go the Rogue route. In the instance that Ranger spells are not a key selling point to playing the class, this is the level progression that I would use.
Ranger 3/Rogue 1-2(depending on your value of Cunning Action)/Ranger 5(boost Dex at 4 and learn PWT at 5)/Rogue X (Thief is the best choice here)
You'll have 2 chances to land Sneak Attack via Extra Attack, have Expertise (preferably Stealth/Perception), be able to Use an Item via Cunning Action, gain advantage on Stealth when moving at half speed, and still have up to 5 ASI.