Breakfast sausage is by far the easiest. I would suggest you start with that. It requires no stuffing into links if you just want patties or to make sausage for biscuits and gravy.
This one is from Michael Ruhlman, it's a good starting point and you can tweak it how you like.
5lbs pork butt cut in chunks that you can grind.
3 tbls kosher salt
5 tbls fresh ginger (peeled and grated or finely chopped)
5 tbls fresh sage
1 tbls minced garlic
2 tsps pepper
Mix it all together in a bowl, chill for grinding, and grind away. Ready to form into patties and throw in your skillet.
Cook a little bit and adjust your seasoning if necessary. Soooo much better than store bought breakfast sausage. It's not even close.
Next, buy a good book on sausage making. My favorite is "Home Production of Quality Meats and Sausage" by Marianski.
The sausage maker website is useful for getting casings, cure, fermenters, tools, etc.