My boy isn't quite 3, and we haven't had any overwhelming problems yet.
However, I'm the oldest of 5, and there are two family units in that (2.5, really, since my half-sister was born 10 years after her next brother), so I've been able to watch a variety techniques.
The forcing techniques turn out the worst, IMO. Food Wars are ugly for the rest of the family. With DH's experience, Food Wars turned him into a food sneak, eating what he WANTED to eat secretly, on top of what he was FORCED to eat. I'm sure you can guess he's got a weight problem.
My half-sis, the youngest, still won't touch anything but chicken nuggets and fries, and she's 12.
The other two, eh, who knows what those young men eat, but there were YEARS of sitting at the dinner table for hours and hours, just utter misery for the rest. (especially since full brother and I were *visiting*, not wanting to deal with arguments, just wanting a nice time)
Making them go hungry wouldn't have worked; they would have just snagged the food they wanted the next day (my dad and stepmom are tall; those kids could reach anything from very young ages). For my full brother, it wouldn't have worked, that boy could go hungry for a LONG time, and he would NEVER cave in.
My full brother only branched into "green food" once he was married, and that only means mom's homemade pesto on pasta. Since she's gone now (7 years today), no more pesto.
Interestingly, I'm the one that was the peacemaker, I would eat my brother's potato when he refused (and my mom went out of the room), I was the one punished by proxy, of having ALL the attention going to the non-eater, today I'm the vegetarian in the family, with various food aversions (during pregnancy it was AWFUL). But I have NEVER made my adult food decisions a problem for any of the rest of the family, unlike their annoying demands and my parents' obnoxious insistences that they eat what was on their plate!
So try to think "big picture", rather than just of today or tomorrow.
Oh, also, I have environmental allergies, and some of my problems are foods that I HAD to eat as a toddler (the family of me and my full brother were in near poverty for years, so the chickens were for eggs and we couldn't waste food), even though I didn't really like them (and wouldn't have eaten if I weren't a peacemaker). Left to my innate responses to foods, I likely wouldn't have eaten those foods.
So I think there's an innate allergy-avoidance in small children, when they refuse to eat things, and I feel that that is worth listening to, rather than forcing the current opinion of "nutrition" on a balking child.