I figured the curly look was your natural hair texture as well! Mine is exactly like that when I leave it to air dry. I can get it curlier if I use product and encourage it, but I rarely do that. I don't often style my hair ultra straight because it takes time and heat styling, and I don't like to put that much stress on it. But I've made peace with the wave/curl over the years, after absolutely HATING it when I was growing up. I now accept it as the way my hair "goes." Many days I simply blow dry the crown and the bangs just so they don't lay weird and let the rest do its thing. I do prefer my hair curly when it has a bit more length to it, rather than when it's freshly cut.
I think its great that you have options for how to style your hair -- it looks great curly or straight. I'm not quite as fond of the really defined curl and the volume at the bottom in the bob in picture #3 -- that look to me seems a little more retro/flapper inspired, which is not really how your style comes through to me. I quite like the sleeker look in #1, as it seems more modern to my eye.
Somehow letting natural curl do its thing can be really polarizing -- I've noticed that when I've gotten feedback on my hair here in the forum, some people express a strong preference for it straight, and others are adamant that they like the curl better. So I'm not surprised that you've gotten mixed reactions from your friends and family.