Should I purchase and use a grease or oil splash screen? I use a sauce pan often for grilling chicken or frying bacon, and a lot of grease tends to splash out. There are fine mesh screens available with a handle designed to cover the pan without creating a seal.

Are these a worthwhile investment, or do they just wind up being one more item to clean?
They are one more item to clean, but they are a lot easier to clean than the walls and stove.

I have several in different sizes - very worthwhile in my opinion.