Using local storage to persist preferences vs server-side session storage

I'm currently working with a web application that has to pass a list of preferences to a java server in order to retrieve a filtered set of data. There are some preferences that aren't being used by the filter that could be excluded entirely from being sent to the server. However, upon page load, we're making a call to the server to receive the list of saved settings to provide some persistence for that user's session.

1. Should the settings that aren't being used by the filter be moved and stored in local storage to minimize latency and traffic or should it be left in the data that is being sent/received for convenience/simplicity?

2. Also, would storing it locally put more work on the client side? This is an important factor as client-side speed is a very important factor.