Hi there-
I do own a juicer although I don't use it much anymore. I made a few veggie juices with it. I didn't like the veggie juices. I like to eat so I eat my veggies plus the fiber is soooo good for you. I made apple juice and carrot juice but again I like to eat those more than drinking them. Plus juice is so rapidly absorbed into your system that I like to just eat my fruits and veggies.
I have a friend who loves her juicer and she juices all the time. I don't think you have to peel anything but citrus. I never peeled apples or carrots or veggies just gave them a good washing first.
I hope you find some good juicing recipes.
There is one I love. I used to take bananas and peel them , freeze them and then run them through the juicer with the solid sheild not the screen (if you have a champion brand juicer). My friend calls it banana whip. It tastes like ice cream. It's so good, but I'm not sure if you eat bananas on your low-carb plan. Have fun trying different combos of fruits/veggies!

Whether you eat them or drink them the live/raw vitamins and minerals are great for your body.