Hi! I love composting and have been doing it for years.
It really depends on what you want from your leftover peels, and what you want for your garden. If you are just throwing leftover peels on the ground, consider what's going to happen to them. Composting is usually contained because it is a great way to attract vermin (rats and mice, esp.) to your home.
Consider getting a basic composter, and do some research online as to which size will fit your needs. Also look online for some DIY ones.
Also, consider the food you are composting. It has to be worm friendly, and worms will love apple, banana, strawberry trimmings, but not citrus. They won't touch citrus and then your compost pile will grow mold, which is also not good for your future soil.
Here's a list of composter reviews... we have a homemade one with an open frame and metal wire mesh on all sides, but it does take longer to break down. Then again, we compost a lot of fruit and veg trimmings. Starbucks is also great for getting big bags of coffee grounds for free. Compost piles love them.
http://composterreviews.com/