Welcome Anton.
Learning on an iPhone will be a bit restrictive due to the small screen size.
If you have an iPad all the better since most of the Apps do tend to have a page or partial page of music displayed and a foot operated bluetooth controller can be used to advance the sheet music. Typically the sheet music is displayed and the play along cursor moves along the score at a fixed but adjustable rate hence the Apps are not best suited for a phone, the bigger the tablet the better.
Check out the Apps:- OnSong, Piascore, forscore and Sheet Music.
Continue doing what you are doing and add a chord at a time but do learn the correct fingering techniques.
I would suggest that you learn C, D minor, E minor, F, G, Am and B diminished but this one is not so well used. Then learn the majors of the minors you have learned & then the seventh’s.
Most pop type songs have a structured format of the form 1, 4, 5 so in the key of C that would be C, F, and G. Many songs are 1,5, 4 so that becomes C, G, F with chords 2, 3 and 6 being included in the song to add dynamics.
Hence in any Key the sequence of Chord types can be Major, Minor, Minor, Major, Major, Minor, Diminished.
Learn these basics and thousands of songs come into the play along mode.
You will find Guitar Tabs a useful site and there are thousands of songs there that someone has transcribed the chords are shown above the lyrics and hence you can play along.
Finally checkout pianogenius.com as he teaches the technique you are following and he has a bunch of free videos available which will show you correct fingering and methods of determining what chord is what, which for a major is very easy with you right hand your thumb is finger 1 and little pinky 5. Thumb on C, 3 on E, 5 on G, now press and hold the notes and look at the number of unplayed notes between each of the fingers playing a note, this is 3 & 2. Choose any note including black notes and replicate the C chord so you have 3 and 2 unplayed notes between your fingers playing the chords. Now you have learned how to play all the Major chords.
