Start with a Half Elf, you need to make sure you have 13 Dex, Wis, and Cha (2 skills)

1st Level Rogue (4 skills)

Then take 4 levels Bard, Lore college, and take the skilled feat at 4th level (5th character level) (1+3+3=7 skills)

Take 1 Level Cleric Knowledge Domain (2 skills)

Take 1 level Ranger (1 skill)

Choose any Background you like that doesn't provide redundant skills (2 Skills)

Math: 2 (Race)+4 (rogue)+7(bard)+2(Cleric)+1(Ranger)+2(Background)=18 Skills

Not half-elf.  Variant human gives you one skill and a feat (Skilled).  17 skills at 6th level and you can grab a feat that gives you one skill and some other stuff when you level up. 

It works either way, I settled on Half-Elf to make multiclassing easier with the standard array,

Don't forget to go up to rogue 11 for Reliable Talent.