I've been trying to play games more frequently instead of passively watching Go lesson videos like I usually do (they are so fun!). I was wondering what game format would be best in letting me improve overall?

I am usually always playing at least 1 or 2 correspondence games at all times, and found that I physically play out many different sequences before playing a move (OGS analysis tool). Results are often better than average in terms of win/loss.

For normal games, which usually takes 40 minutes or so, I usually don't have time to place stones on the board to analyze, so this requires mental reading. Win/loss is usually 50/50 taking rank difference into account.

For blitz games, I think I lose 2 or 3 stone strength when playing, making fatal mistakes often.

This led me to think I need much more practice in blitz games, but people have been telling me that blitz games often reinforce bad habits and might create new ones.

What is your opinion on what the best format is for training purposes? What do you usually play?

A mix of thinking times of various lengths is best. In blitz you should experiment new things. Then if you find something promising, you can try it in a long thinking time game and try to read what happens. An occasional blitz game agains a stronger player is fine. Yu might get immediate feedback on a position which you have been reading with longer thinking time.

My opinion is that you should optimize for the time settings you want to be successful for. If a tournament is coming up with 30 minutes main time, practice under similar settings.

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be immersed

I like both the advice you received.

In my understanding, playing games with a length that gives me the opportunity to plan my game and express the best Go I can is (most) important; still it requires more time and energy than I usually have at the end of the day.
Playing faster games, helps me to understand where my general knowledge is not so solid.

Both are a good way to improve, as far as one takes the time to review and learn from his mistakes (possibly with a stronger player at his side to help).

When training for a competition, or a test as well, focusing in the same conditions I will be tested in, is a good idea.
I usually prefer the conditions to be just a little harder, so that I will feel comfortable and ease the tension of the event,

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When you play Weiqi you are joining millions of people across four thousand years of time.
Jonathan Hop - So You Want to Play Go?

I know someone who says that when he was a SDK, playing blitz games and reviewing them afterwards helped him identify his shape problems. I haven't tried his method on myself: when I play blitz, either I lose on time, or I miss easy life-and-death problems, that's too frustrating so I rarely play blitz games.