If you want to change the associated contenttype for a pagelayout, you can do it like this:

// first you need a reference to a PublihingSite or PublishingWeb
var pubSite = new PublishingSite(site); 

// then we need to get all available pagelayouts
var pageLayouts = pubSite.GetPageLayouts(false); 

// try to find the pagelayout you want to update
var pageLayout = GetPageLayout(pageLayouts, "pagelayout.aspx"); 

// if pagelayout exists, update it (here you need to have a ref to the contenttype)
if (pageLayout != null)
    UpdateAssiciationContentType(contentType, pageLayout); 

/// <summary>
/// Helper method to update associated contenttype for a pagelayout
/// </summary>
/// <param name="newsContentType"></param>
/// <param name="pageLayout"></param>
private static void UpdateAssiciationContentType(SPContentType contentType, PageLayout pageLayout)
{
    // Check out the pagelayout
    pageLayout.ListItem.File.CheckOut(); 

    // set AssociatedContentType
    pageLayout.AssociatedContentType = contentType; 

    pageLayout.Update(); 

    // CheckIn, Publish and approve changes
    pageLayout.ListItem.File.CheckIn("Changed associated contenttype");
    pageLayout.ListItem.File.Publish("");
    pageLayout.ListItem.File.Approve("Change approved");
} 

/// <summary>
/// Get pagelayout by name
/// </summary>
/// <param name="pageLayouts"></param>
/// <param name="name"></param>
/// <returns></returns>
private static PageLayout GetPageLayout(IEnumerable<PageLayout> pageLayouts, string name)
{
    var layouts = from PageLayout layout in pageLayouts
                  where layout.Name == name
                  select layout; 

    return layouts.Count() == 1 ? layouts.ElementAt(0) : null;
}

Out of the box SharePoint has a few content types that you can use. If you would like to create your own that inherits from one of these you could do it like this:

// first we reference the content type we want to inherit from
SPContentType pageContentType = web.AvailableContentTypes[ContentTypeId.Page];

// create our new content type
var customContentType = new SPContentType(pageContentType, web.ContentTypes, "Name of content type");
newsContentType.Group = "Custom content type group";

// add content type to the site
web.ContentTypes.Add(customContentType);
web.Update();

To add a custom sitecolumn to our new content type:

// first we need to find our site column
SPField siteColumn = web.AvailableFields.GetFieldByInternalName("InternalSiteColumnName");

// Add column to our new content type
customContentType.FieldLinks.Add(new SPFieldLink(siteColumn));

// Update content type
customContentType.Update();