The Browser Automation Guide contains all the recommendations for that interface about the best attributes to use.
No matter what interface is used, think of it as a large underlying treeview navigation through the applications model to the element you want to find. So with the browser interface if you did not have the Path ticked Blue Prism would navigate the web page model to find every element and then decide if the attributes for that element matches the attributes you have ticked for your element.
The HTML Path is like a direct mapping of the path that needs to be taken through the underlying application model to get to the element you want, so rather than having to go down every tree it knows how to navigate in advance to where you want - that massively speeds up the interface.
One thing to watch out for is that you should never just have the path ticked if at all possible. Ideally you will still have some other attributes ticked that would uniquely identify your element, just in case the path to your element ever changed - you would not want to have a path to an edit box that ended up being the path to a different edit box!
The Browser Guide also mentions the ID attribute as sometimes being usable to speed up the interface (it is like a key field in the underlying IE DOM). Also Match Index speeds up all interfaces, and Accessibility Mode often works well for browser applications.