I agree with emeraldarrows about Splash splash love! I feel like it's a perfect "dip your toes in" historical drama, since it has both the modern (ish, it's from 2015) world and more of a "traditional" historical drama without making it silly. It's actually very sweet.
Since you said you liked more modern dramas, I'd also like to recommend:
Hi Bye, Mama! - sweet and a little bit sad, deals with loss/grief with a slightly unusual twist
Hello, Me! - heartwarming and healing, themes of trauma, healing your inner child, letting go of guilt etc
See You In My 19th Life - a little bit melancholy but also beautiful? a girl who remembers her past lives tries to watch over/reconnect with people she loves (who don't know her anymore because she's not the same person). calm and slow paced but definitely worth watching.