I lived in Korea and have tested a lot of great products. Let's go by step for the stars I've stuck with.
Cleansing: Dr. Jart's Micellar Water is my favorite. Son & Park Beauty Water is amazing but not sold on Sephora.
I use Sulwhasoo Gentle Cleansing Oil and follow it with Clinique Liquid Facial Soap.
Toner: For moisture, I like the belif Aqua Bomb Toner; it's very moisturizing. Most Korean toners are moisturizing, so if you want a more acidic one, I don't recommend any Korean brand.
Essences, Serums & Ampoules: The Sulwhasoo line is great; I especially recommend the First Care Serum. I apply that before anything else. Danahan makes great ginseng essences and emulsions. Neogen H2 Dermdeca Serum Spray is a really refreshing mist serum. Mizon's entire ampoule line is fabulous.
Sheet Masks: Here's the wild thing about sheet masks in the US versus South Korea: in Seoul you can get 10 masks for 5-10,000 won aka $4-9. Innisfree has a nice mask club where it's 30masks/$40. I mask almost every day for moisture, as did every Korean girl I knew. We'd have soju and snacks while applying masks and doing our hair before going out. So mask up! Peel masks aren't good for my skin, but Dr. Jart+ rubber masks were favorites of my oily-skinned friends.
Lotion: The Mizon Black Snail All In One Cream is great, but not enough for dry skin, best for normal/combo. The belif Aqua Bomb is also one of the best I've tried for staying fresh. Dr. Jart Tiger Grass Color-Correcting Cream is nice to treat redness and has SPF.
Eye Cream: The belif Moisturizing Eye Bomb goes really well over my retinol eye products. Missha Cho Bo Yang Ginseng Eye Cream is my favorite nighttime eye cream... a little goes a long way.
Treatments & Sleeping Masks: Neogen makes THE BEST exfoliating pads, the BioPeel Gauze Pads. I use them 2x/week; the chemical toning and the two-textured pads make skin feel baby-smooth after a soft scrub. For sleeping, I do like the Laneige Water Cream (normal skin) or Cica Cream (dry skin) and from Sulwhasoo, the Overnight Sleeping Mask. I also love Mizon Intensive Gold Eye Mask gels as a daily morning staple. Cheaper than the Peter Thomas Roth Gold gel masks. The Laneige Lip Sleeping Mask is the best. Second winter I've used it every other night and the second during which I've never ever had chapped lips.
NOTE: Most Koreans I knew all bought a specific toner... the Origins Mega Mushroom Treatment Lotion (which is a non-alc toner). Just like K-Beauty is trendy here, Clinique and Origins (the Estee Lauder giant) are super desirable there. And even though Glow Recipe is branded as Korean Skincare, it isn't. It's similar to Peach & Lily's line... Korean-Americans building great companies by capitalizing on a trend. Not bad products, but dissimilar testing and priorities. AmorePacific is THE beauty giant (kind of like Estee Lauder owns loads of brands in the USA), so look under them for the most-tested products (Sulwhasoo, Laneige, Innisfree, Primera, Iope, Aritaum)...
Origins Dr. Andrew Weil for Origins™ Mega-Mushroom Skin Relief Micellar Cleanser 6.7 oz/ 198 mL
SULWHASOO - First Care Activating Serum SULWHASOO - Gentle Cleansing Oil
CLINIQUE All About Clean™ Liquid Facial Soap Gentle Cleanser 6.7 oz/ 200 mL Mild
BELIF - The True Cream Aqua Bomb
belif Aqua Bomb Hydrating Toner with Hyaluronic Acid 6.75 oz/ 200 mL
BELIF - Moisturizing Eye BombDR. JART+ - Lover Rubber Masks
Dr. Jart+ Cicapair™ Tiger Grass Color Correcting Treatment SPF 30 1.7 fl. oz/ 50 mL
LANEIGE Lip Sleeping Mask Intense Hydration with Vitamin C Berry