Synopsis, genre and if the trailer is interesting enough for me.
Sometimes I watch it because of actors/an actor that I like, but I can also choose to not watch a drama if the actor was in the drama I've watched in the latest one because I want to se other actors lol
Sometimes I watch a drama that someone recommend me, but that's rarely
I don't watch dramas so often, I think I've watched more movies than dramas
I pick at random and I don't read the synopsis or look at the actors. I do however look at reviews sometimes but generally I pick shows up at random. 
First, sypnosis, secondly the actors
First of all because of the plot and genre, then I look at the actors. Sometimes when I miss seeing one of my favorite actors for a long time and finally a new drama is coming, I just don't care about the plot at all because I can finally feast my greed with looking at the actor alone :'D
Genre, good actors, storyline/plot and ending...I hate watched things that have bad ending especially if my favorite character died. So i will go and checkout the spoilers  first....
- Actors (if I specifically search for an actor, I will go through their dramas first)

- Storyline/Genre/Characters (I try getting something out of the summary, then I carefully check out the reviews and comments - Beware of the spoilers)

- First 15 minutes (It seems interesting, so I check it out. If I'm not hooked and there's no reason to continue - Favorite actor, great reviews, some storyline I heard about and want to see -, I will stop.)
Great actors is a must from me.
I choose a drama based on a number of things:

Plot/Characters - I have to like the sound of the story or at least be a little invested in the concept. Some of the characters have to also be likeable :)
Actors - Of course, if I have a certain actor I'm biased towards I do tend to check out their drama first...
Genre - I tend to prefer certain genres and though I will dabble with others I'm less interested in I do tend to watch the ones I like first..
1. Plot
2. Length - should be not less than 30 eps unless it's really good or popular
3. Ambiance - some ambiance of dramas bore me. mostly mbc dramas have those boring/makjang ambiance. if you know what i mean..
4. Actors - I don't look at their face, their acting and voice are what make me love or drop the show
5. editing - some shows have really messed up editing, it makes me dizzy
1. My Mood ( genre )
2. Quality
3. Synopsis
4. Promotion image
5. Actors
1) plot
2) overall chemistry of the cast 
3) actors (I will break my 3 episode rule if one of my favs is acting in a drama/movie)

I usually give a drama 3 episodes to draw me in :P
If the plot suits my taste and sometimes because of who is in it.
plot and length mainly
casting is no important...
synopsis and genre .. also the first 4 ep will help me see if the drama is worth watching or not