When you learn these chords, it's also worth observing which notes are essential for its sound and which ones aren't. When you're in a band situation, you can many times eliminate playing the root and 5th. The bass usually plays the root, the 5th doesn't necessarily add much soundwise.
One complaint that other musicians have about pianists and keyboardists is playing too many notes. If you're in a solo situation, that's different since only you are there to supply the accompaniment and melody. When we're in a band with 10 fingers that can hit 10 and even more notes, we need to step back and figure out which notes really matter and which we can discard especially to not step on other band members.
At first we need to think about this a lot, yet with practice and repetition it'll become as natural as other languages. You'll spot a chord symbol and already know by instinct how you'll position your hands, whether you'll go for an open or closed voicing.
You can also experiment with the different inversions of the chords and see how they feel and sound for you. And sometimes you'll discover the inversion of one chord works in place of another chord because both chords have the same notes, just different "spellings."
It's definitely worth getting to know inversions for several reasons. First, there's a big temptation to always play things in root position when we look at notation. Yet the music needs to sound smooth. That's achieved nicer when chords go from one to another without jumping around. (Look into the concept of "voice leading.") Second, it makes fingering easier. It's necessary to do this when playing keyboard instruments.
One other thing that is extremely helpful worth trying. If you find a piece of music you like that does NOT have chord symbols on it, write them in. See how the chord symbols you came up with match up with the song. Does it sound sensible? One piece I saw this with was the 1st movement of Beethoven's Moonlight Sonata. It was really interesting to see that C#m then C#m/B as well as the rest.
Many times when I want to understand what's going on with a piece, I write my own chord chart. You can also do this for songs on the radio like the modern pop things you're speaking about. See how close you get. What chords are those songwriters using? (Sometimes you'll absolutely have to do this if the composer has not released any sheet music.)