I find that my playing changes completely when I am also singing - and it doesn't matter what instrument. On uke I can do really nice arpeggios and stuff until I start singing - the moment I start singing I drop into a very simple strummed accompaniment and that seems to be all I can manage. If I try to sing while I am playing bass I inevitably end up crashing and burning.
I think when I sing that that part of the music takes over my brain so I can only do relatively simple things with my hands.l
I'm honestly probably a little better singer than instrumentalist (though I'm nobody's hero on either) but I've seriously considered giving up the singing to concentrate on being a better picker.
I don't know if this came close to answering your question - but the bottom line is to have fun and do what you feel you need to.
Most people are harder on themselves than they really should be, especially as regards voice. Part of this is because what we hear in our heads when we sing is not what everybody else hears or what gets picked up by a microphone. The first time I sang using a PA with monitors was absolutely dreadful - I kept trying to make what was coming out of the monitors sound like the "me" that I hear in my head with bone conduction and so on and the result was predictably awful. Since, I've learned to either ignore the monitor entirely or treat it as if it were another person singing with me and as long as what I hear is on pitch I'm happy with that.
Finally, when it comes to "good" voices vs. "bad" voices a lot depends on several factors - some of which are necessary and some of which are optional. The most important factor is to be on key - put your initial efforts into developing your ear so you know when you are on pitch or off pitch. It doesn't matter what a wonderful crooner you are if your twenty cents off pitch or reaching for notes that you can't get to with a ladder.
That is 90% of the battle. However, that last ten percent is often the difference between a singer that people can tolerate and one that they will go out of their way to hear. I know a semi-pro singer/songwriter who writes wonderful songs but the poor gal insists on singing them herself. She is perfectly on pitch pretty much 100% of the time - but her voice is just dreadful - she sounds like a wife nagging in key. Honestly, if she was doing hard blues or rock she might do well but for the stuff she writes nobody buys her albums because there is a complete disconnect between the timbre of her voice and the material she is singing and the accompaniment she is using.
Finally, most beginning males tend to sing below their ideal range and most beginning females tend to sing above their ideal range. Not sure what's going on there but it seems to follow. You shouldn't sing in your speaking voice, nor does your speaking voice necessarily indicate what your best singing range is. My speaking voice is very low, my best singing range seems to be high baritone to low tenor - I can occasionally pull off bass but only if they are very short supporting harmonies and not sustained notes. THe leader of our band also has a low speaking voice - speaking he can make the subwoofer rumble - his best singing voice is high tenor and he can even pull off the soprano when he needs to help the female vocalists get their harmonies down.
Lastly, I'm
not a singer nor a vocal coach so please feel free to ignore absolutely everything I said above! (I did, however, pay for two years of private lessons for my oldest daughter and I learned a lot from her teacher when she thought I wasn't listening. LOL)
John