301 vs 302 Redirect in a search function

Hey all! I tried googling this but unfortunately couldn't find results. That, or I'm just not interpreting them properly.

So I'm working on this website that uses an old framework where a search function update was implemented. From the homepage, the user fills up a search form. The system initially takes all the search parameters (URL: /pre-search?<parameters>) provided by the user then forwards (redirects) them to the appropriate search page. Example:

If user searches location + category, redirect them to a location + category page. If user searches for location + category + subcategory, redirect them to a location + subcategory page, and so on.

Right now the framework uses 302 redirect by default. Would 301 be better for this?

Or if the whole approach is bad, what would be a better way to implement this search feature?