在使用NuGet进行搜索时，可以使用PackageSearchMetadata类中的DownloadCount属性和LastUpdated属性来对搜索结果进行排序。以下是一个示例代码：

using NuGet.Common;
using NuGet.Protocol;
using NuGet.Protocol.Core.Types;
using NuGet.Versioning;
using System;
using System.Collections.Generic;
using System.Linq;
using System.Threading;
using System.Threading.Tasks;

public class Program
{
    public static async Task Main(string[] args)
    {
        string searchTerm = "your-search-term";
        int pageSize = 100; // 每页显示的结果数量

        // 创建NuGet源资源提供程序
        SourceRepository repository = Repository.Factory.GetCoreV3("https://api.nuget.org/v3/index.json");

        // 获取搜索资源提供程序
        PackageSearchResource searchResource = await repository.GetResourceAsync();

        // 创建搜索查询
        SearchFilter searchFilter = new SearchFilter(includePrerelease: true);

        // 执行搜索查询
        IEnumerable searchResults = await searchResource.SearchAsync(searchTerm, searchFilter, skip: 0, take: pageSize, log: NullLogger.Instance, cancellationToken: CancellationToken.None);

        // 对搜索结果按下载次数和最后更新时间进行排序
        searchResults = searchResults.OrderByDescending(p => p.DownloadCount).ThenByDescending(p => p.Published);

        // 输出搜索结果
        foreach (IPackageSearchMetadata package in searchResults)
        {
            Console.WriteLine($"Package Name: {package.Identity.Id}");
            Console.WriteLine($"Download Count: {package.DownloadCount}");
            Console.WriteLine($"Last Updated: {package.Published.LocalDateTime}");
            Console.WriteLine();
        }
    }
}

请注意，此示例使用NuGet.Protocol和NuGet.Common包来执行NuGet操作。在使用之前，需要将它们添加为项目的依赖项。