I'll be back later with some recommendations, but my first bit of advice is to watch dramas with people you want to talk like. Listening practice is one advantage of watching dramas, but like it or not you will also end up emulating the speech as well.
Japanese changes a lot based on gender, age, socio-economic class, location (part of Japan), etc. So you want to choose wisely who you will copy.
As a teenage girl, just because you like to watch Yamapi or Yamada Ryosuke, doesn't mean you should also aspire to talk like them.
As a thirty something woman, you may like watching school dramas, but you probably shouldn't copy the teenagers, male or female.
And as a beginning learner, it's best to stay away from dramas set in Osaka or Kyushu, or anything involving Kanjani 8. (As listening practice anyway... first you won't be able to understand them, and second you should probably stick to standard Japanese for speaking in the beginning. Of course watching them for entertainment value is another story)
If you are a guy, especially if you are studying formally with a female teacher, you should watch things with lots of male characters. That is the one thing that all of my guy friends noticed when they went to Japan. As most of the native speaking teachers in the US are female, they got to Japan and were told their speaking was very effeminate... oops...
