I totally agree with others here - UML is not a process. You need process and notation, and UML is a tool for the second.
Gathering requirements can be as agile and iterative as building the code.
The Use Case diagrams are a very high level summary. Behind each ellipse there are a number of scenarios. If you know the overall goal, you probably can intuitively identify a number of use cases, and you should write them down and build a first draft rough. And you can start to give them priorities, and start to map out scenarios.
Sooner or later, you'll refine use cases and scenarios. A sequence in a scenario might deserve to be a use case in its own right. Two use cases might be similar enough to merge into one. A use case may not really achieve a goal, so again it should be merged.
If a Use Case diagram is so high level, what's the benefit? Use Cases should deliver a goal for an actor, so they help us focus early on systems that are useful from the perspective of our users. They give us a list of discrete requirements that we can start to prioritise. When we reprioritise, we have units to trade off ("If you really want your pet use case Pay Supplier, you'll have to wait longer for this other use case Pay Salary"). When we prioritise up or down, it's easy to see which actors will be advantaged and disadvantaged.
The old advice to "underline nouns and verbs" is more about your scenarios. There's probably not enough detail in the Use Case diagram to identify candidate classes.
So as a starting point, Use Case comes before scenarios, but only as a starting point. There will be iteration and feedback as you work on your system. Similarly, scenarios come before classes as a first cut. When you get as far as operations, they should be organised into classes. So as a starting point, classes come first. When you identify an operation and it's not obvious where it should go, likely you'll create another class that you hadn't thought of before.
Activity diagrams are high level business process diagrams so may come earlier to communicate about your scenarios. Sequence diagrams document the behaviour of your operations and the classes and objects involved, so overall they'll come a bit later. Note that the UML Communication diagram shows similar information to the Sequence, but from a different perspective - time is easy to see in Sequence, the objects themselves have priority in a Communication diagram.