MVC 3 form post and persisting model data

I think I'm missing some fundamentals on how MVC forms work. I have a search form on my home page that has five or six different fields a user can search on. So I have this POSTing to my results action just fine. The Result action looks like this:

[HttpPost]
public ActionResult Results(SearchModel model)
{
    ResultsModel results = new ResultsModel();
    results.ResultList = SearchManager.Search(model).ToList();

    return View("Results", results);
}

I've simplified the above method for this post, but the idea is the same. So this all works fine. My results page shows up with the list of results and my user is at the following URL:

http://www.site.com/results

So...now I want to do something fairly common. I have two dropdown lists on the results page. "Sort by" and "# of results per page". How do I do that and send the full set of model data back to the controller so I can query with the new parameters? In reality, the SearchModel class has about 60 different fields. Potentially all of that data could be contained in the model. How do you persist that to a page "post back"?

This same question has me a little stumped about how to do paging as well. My paging links would go to a URL like:

http://www.site.com/results/2

But that assumes that we're responding to a GET request (I don't want 60 fields of data in the querystring) and that the model data is passed between GET requests, which I know isn't the case.

As I said, I think I'm missing some fundamentals about working with MVC 3, models and form posts.

Can anyone help point me in the right direction here? I'll be happy to edit/update this post as needed to clarify things.

EDIT: I also wanted to point out, I'd like to avoid storing the view model in a Session variable. This site will eventually end up being load balanced in a web farm and I'm really trying to avoid using Session if possible. However, if it's the only alternative, I'll configure another session state provider, but I'd prefer not to.