Like the title says, I've seen movies, but not really TV shows. So can somebody recommend me some good ones for starters? I like almost every genre, but I do especially like thrillers, psychological, comedy, action, adventure.

I think you'll find about everything in You're All surrounded.

You can also try :
- I Hear Your Voice : Thriller / Fantasy / Kdrama / noona romance. About lawyers but it feels more like a detective drama, also the guy can hear what people think.
Call of the Country : Romcom / Police Kdrama. More of a comedy than a crime drama.
Love Me If You Dare : Cdrama / Police / Thriller / Romance. The cop is a profiler if I remember correctly.
- I Remember You : Kdrama / Police / Thriller / Romance. Also a profiler.

There are also two others I'd like to recommend. But don't start with them or you might end up in a slump :
Signal : Kdrama / Police / Fantasy. Two cops communicate through time with a walkie-talkie. (Kind of like the movie Frequency) Profiler.
When A Snail Falls in Love : Cdrama / Police / Romance. Again, profiler. It's the trend ;)
I don't watch a lot of action but for some stuff you might enjoy, try...

99.9: criminal lawyer 
border
cruel city (slow-paced but intense)
white christmas
healer (slow start, give it 4 or 5 eps. has a little bit of everything for everyone.)
ishi no mayu + sequel suisho no kodo
liar game (jdrama)
liar game (the k-adaptation. personal preference, but I prefer this version)
missing noir m
seirei no moribito
yokoso wagaya e

other stuff I have not watched or have paused but hear good things about & might be up your alley are bridal masksignalyou're all surrounded38 task forcebad guysmy beautiful bride, & mask.
These mainly fit the psychological, action, or thriller genres... (Edit: they're all quite depressing too now that I think about it).

Maou
Little Girl K
Kazoku Game
Byakuyako
White Christmas