I didn't see it so if I am posting it again sorry- but you should watch My Name is Kim Sam Soon aka My Lovely Samsoon

snow white / full house

If you haven't seen Damo, then I think that's a good drama, it's a historical one. My Girl and My Sweet 18 are two contemporary dramas that are good too. Delightful Girl Choon-Hyang was a cute one too. There's a few others that I like but I can't remember the names right now.

I've also just begun watching Korean Dramas...

Witch Amusement/Witch Yoo-Hee was the first ever one I watched. Thats a good starting point. Then came Goong, you seriously need to view that.

I've just begun watching My Lovely Samsoon/My Name is Kim Sam Soon. Its hilarious!

Why not try for My GIRL & stairway to heaven.

Just nice story.....

Apart from the ones that's already being mentioned, how about:

Green Rose
1% of anything
Lovers in Paris
Princess Lulu
Snow Queen
Autumn Showers
Delicious Proposal

They are all pretty good and I have enjoyed all of them.

You should see 200 pounds beauty, it's quite good.
As for series, you should watch:
Goong
Memory of Bali
Wonderful Life
A Love to Kill
My Girl
My Name is Kim Sam Soon

These are really great dramas:

fantasy couple, goong/princess hours, delightful girl chunhyang, my lovely sam-soon

Stairway to Heaven

smiling pasta was a good drama
if you like other dramas that are cute funny sad all at the same time, you should watch this one.