A Feature Class can only take feature classes via a path, but gives you guaranteed access to the data definition (fields, indices, attribute rules etc.).
A Feature Layer can take a feature class by path or a layer from the current map. You can't always edit the structure of your data but you can edit its features, and the user can pass in a subset of the full data.
A Feature Set can take all of the above plus arbitrary feature data from any source. But it's even less likely that you can modify the data's structure.
In short: as you go from FC to FL to FS it becomes harder for the user to specify what exact data is edited but the script has an easier time modifying the data. I usually go with Feature Layers if I don't have a specific use case but it's up to you.
(Note that Table, Table View and Record Set are the non-spatial types of their respective parameters. This doesn't stop you from passing in spatial data but you lose the guarantee that you can work with the data's coordinate system, geometry data etc.).
