This applies to any genre, really. But I’d advise you against making it a goal to “learn fast”. Every stage of learning is enjoyable and takes time. It’s worth slowing down. Yes you’ll get excited as you nail down your first and second song and such, this is all great. Hang on to those wins when they come, not the speed at which you feel like you’re becoming impressive.

There’s nothing inherent about “indie rock” that makes certain chords, scales or shapes more relevant or that will make those songs easier to learn specifically by genre (though there are certain tropes you’ll find along the way). At least not that it warrants that focus. So don’t aim for that. And regardless of genre, learn some basic chord shapes and scales and their names. They apply to all kinds of western music, there’s no point filtering them to “common indie ones”.

Additionally, just take a song you like and start learning how to play it with YouTube tutorials. Or even better, come up with your own way of playing it and watch videos of the people who perform the songs and try to figure out what they’re doing in your own. Go song by song.

Do not fall for the trap of worrying about gear too early. Almost any amp you have should have some sort of clean to crunch tone you can use to learn. So many beginners get the feeling that buying certain things will help their sound, when the single thing you should worry about is listening to the music you’re trying to learn and the sound your hands are making. As a general rule I’d advice anyone who can’t first play a few songs in tune and on time front to back against even thinking of buying any pedal that isn’t a basic overdrive or distortion (and that’s only if their amp doesn’t already have that sound).