Question: I am tired of using canned broth/stock and would like to make my own - any suggestions as to the proper technique and parts to use?

Answer: 
In general, the parts of the animal to be used in making stock depends on the animal:

For chickens, different people will recommend different parts of the animal, but simply chopping up an entire chicken works fairly well.

For beef, pretty much any tough piece of meat will work; try looking at shoulder or butt.

As for other suggestions, be creative! Almost anybody can make a basic broth by boiling a chicken, but making one that is truly fantastic takes time and work. Try adding different ingredients. For starters, try things that you are familiar with. For example, vegetables and herbs like garlic and basil can improve any broth. From there, try things that are more creative, like sesame oil, miso paste, or perhaps ginger.
We start with our older laying hens & roosters. remove Head, dip in boiling water pluck chicken. Next gut. Place aside giblets. Wash in cold well water. Place in large pressure cooker. With salt, onion chopped, garlic, pepper, morening leaf. Feet may be left on. Cook 4 to 6 hours till meat falls of bones. Cool. remove grease from top. Remove all bones. Large chunks of chicken cut up. Taste broth. You may wish to add more spice. Put pot back on stove boil to reduce till you have flavor you wish. Cool. Put in bags. Remove all air. Use masking tape & pen to label bags. Freeze till needed. The secret to good chicken stock is to not use fryers or bakers but your older chickens free range ones.