I've reached a point where I need to sing so I can enjoy my guitar journey. My problem is I feel my voice isn't good enough and to coordinate both singing and playing is still an issue unless I'm singing along with chords and lyrics of a song, mostly covers by some other guys. How do I develop independence so I can sing on my own?
The process you have to go through is very hard, like automatisation of driving a car, like the independencity of the hands and fingers when playing piano.
- Try to hum along the melody when playing guitar (the guitar playing must be on a high level.
- Sing the song with lyrics only clapping with your hands (this will already be a pretty effort!)
- Sing along with the Guitar accompaniment only strumming the strings.
- Sing also off-beat and in free rhythm (groovy) when strumming on the Guitar.
- Try to sing with finger picking and arpeggio accompaniment (humming and then with lyrics).
You say you can sing and play at the same time when doing covers. Maybe this means that you're simply more familiar with the covers than with your own songs, and just need to keep playing them more?
Also, "my voice isn't good enough" is somewhat a different issue. If you mean "I can sing with a projection and tone that I like when I'm not also playing," then that makes sense, and will benefit from all the exercises Albrecht suggests. If you just mean that you don't like your voice in general, then feel free to seek improvement and growth, but you might also need to simply learn to love your own voice. I would argue there's no such thing as "not good enough"; it sure never stopped Bob Dylan! Every voice is distinctive, and finds its own audience. No harm in cultivating and training your abilities, but at some point, your own sound is the product of the vocal cords, lungs, and sinuses you were born with, and your commodity is yourself.
If you don't manage to play guitar and sing at the same time with the songs you're currently trying, try it with simpler songs. If it still doesn't help, try it again with even simpler songs.
If it's a song with only 1 or 2 chords, and simple strumming on each beat, so be it! You'll have plenty of time to try more complex songs once you master the easiest ones.
The first song I played and sung at the same time was from Juno soundtrack : "Anyone else but you", with G and Cmaj7 chords.
You might find that some complex songs are somehow easier for you than for other people, so keep on looking for songs that seem natural to you! There are many songs which have distinct rhythms for guitar and lyrics, and it's a real struggle to play them (e.g. Alabama Song - The Doors, Forever - Ben Harper, or Do I wanna know - Arctic Monkeys).
Singing loudly in a large space where you want to make yourself heard is much, much easier than singing quietly in a confined space where you don't want to disturb the neighbours. Even in performance conditions, singing quietly is much harder than singing loudly. That's because to sing well, you need to breathe deeply, and it's much easier to control the flow of air when you're projecting your voice well. The problem if you "think your voice isn't good enough" is that it probably means you are trying to make sure you aren't overheard, which is the opposite of what you should be aiming for.
Another problem might be that you're recording yourself and listening to the recording. If you have a sensitive ear, you're almost certainly going to hear that your voice wasn't very accurately pitched. But that can lead to a spiral of decreasing confidence. A singing teacher would work on your pitch by working on your posture, your relaxation, and your confidence, not by telling you you're getting it wrong. They would also work on exercises explicitly designed to improve your pitch, for example by modifying the vowel sounds. It's hard to replicate that if you're working on your own.
My advice would be, don't do this on your own. Sing with others, ideally with a teacher, in an environment where you can make a noise and not be embarrassed by it.
I wasn't making much progress on singing until I started working with a teacher. But it must be the right teacher. If you want to sing pop music and your teacher wants to teach opera, that's not going to work.
Also, my teacher had to struggle to learn how to sing. It didn't come easily to him at all. Someone like that will be much more understanding of your difficulties with the basics. That was just what I needed.
You may have to try several teachers before you find one you like, and where you feel you are making progress.