I find the easiest way to distribute oil on the phyllo sheets is to use a sprayer. I have a Pampered Chef kitchen spritzer I’ve nursed along for years but there are also lots of similar beasts on Amazon. Don’t expect an oil pump to make a fine aerosol but they do a good job of making a little oil go a long way. I keep mine filled by the stove and use it whenever I want to keep things from sticking. When it clogs, I soak its parts in hot water and detergent and then run them through the dishwasher.
Olive oil works equally well for sweet or savory recipes. You can always drizzle on some melted butter on some layers if you want that flavor. Using the sprayer tends to make a less fatty pastry which some may find too flaky-crispy.