I don't think there is a minimum for sugar and carbohydrates (that's why low carb diets can work) but there is a recommended minimum for protein. Professional athletes etc. base it on bodyweight, but a general minimum for women is about 50g I think. I use the recommendations by the Mayo Clinic and they work well for me:
End the guesswork.
I found when I started hitting that protein minimum, by including some protein and a little fat at every meal, I was less hungry. But I am also a big carb processer personally, so if I fall below a certain amount of carbs for several days in a row I run out of steam in my exercise. So I go for a minimum of protein first, then a minimum of fibery vegetables (it helps my, er, internal processes) which also pack some carbs. So plan my meats/fish/beans/cheeses and then veggies, and then it's not really a problem to fill in what's left with fruits and whole grains because I could easily eat too many of those. One thing that makes it easier to get lots of different vitamins/minerals is to think lots of different colors: not artificial but natural — a variety of different colored vegetables and fruits. If there is something particular I am regularly low in, sometimes I will google "Vitamin E source" or whatever. OK, sunflower seeds, I could work those in somewhere —*on top of salad?
You also need some fats to process certain vitamins (fat-soluble vitamins). While I was dieting I tried to keep fats under 30% of total cals (because of the higher calories) and now I range between 30-35% usually. Of course there are lots of different ways to portion out your protein/carbs/fats and different ratios work for different people, so you want to try one way for a couple weeks and then another way to see if one makes you feel better/less hungry etc.
I use the LoseIt app and it makes it easy to track the main things, although unfortunately you can't do vitamins on there. So occasionally I check them on fitday. I don't hit them all exactly every day, but with going over some and under others day by day I generally average out properly during the week, except for iron. So I take a multivitamin about once or twice a month. I don't take it every day because it doesn't always agree with me, and your body just passes through most of those vitamins if it doesn't need them — like you said and as one of my nutrition sources pointed out, just "expensive pee"!
ETA: If you want to get SERIOUSLY into percentages of nutrients Lyle McDonald's web page is a good place to start: you can get a taste of how he lays things out in an article like
Diet Percentages Part I. He is mostly interested in fuelling and training athletes in various ways but also has some good stuff on weight loss and training beginners.