I've done this kind of thing before, and ended up with a nice toolkit for writing these types of applications. I've used this toolkit to handle non-trivial back-n-forth web requests, so it's entirely possible, and not extremely difficult.

I found out quickly that doing the HttpWebRequest/HttpWebResponse from scratch really was lower-level than I wanted to be dealing with. My tools are based entirely around the HtmlAgilityPack by Simon Mourier. It's an excellent toolset. It does a lot of the heavy lifting for you, and makes parsing of the fetched HTML really easy. If you can rock XPath queries, the HtmlAgilityPack is where you want to start. It handles poorly foormed HTML quite well too!

You still need a good tool to help debug. Besides what you have in your debugger, being able to inspect the http/https traffic as it goes back-n-forth across the wire is priceless. Since you're code is going to be making these requests, not your browser, FireBug isn't going to be of much help debugging your code. There's all sorts of packet sniffer tools, but for HTTP/HTTPS debugging, I don't think you can beat the ease of use and power of Fiddler 2. The newest version even comes with a plugin for firefox to quickly divert requests through fiddler and back. Because it can also act as a seamless HTTPS proxy you can inspect your HTTPS traffic as well.

Give 'em a try, I'm sure they'll be two indispensable tools in your hacking.

Update: Added the below code example. This is pulled from a not-much-larger "Session" class that logs into a website and keeps a hold of the related cookies for you. I choose this because it does more than a simple 'please fetch that web page for me' code, plus it has a line-or-two of XPath querying against the final destination page.

public bool Connect() {
   if (string.IsNullOrEmpty(_Username)) { base.ThrowHelper(new SessionException("Username not specified.")); } 
   if (string.IsNullOrEmpty(_Password)) { base.ThrowHelper(new SessionException("Password not specified.")); }

   _Cookies = new CookieContainer();
   HtmlWeb webFetcher = new HtmlWeb();
   webFetcher.UsingCache = false;
   webFetcher.UseCookies = true;

   HtmlWeb.PreRequestHandler justSetCookies = delegate(HttpWebRequest webRequest) {
      SetRequestHeaders(webRequest, false);
      return true;
   };
   HtmlWeb.PreRequestHandler postLoginInformation = delegate(HttpWebRequest webRequest) {
      SetRequestHeaders(webRequest, false);

      // before we let webGrabber get the response from the server, we must POST the login form's data
      // This posted form data is *VERY* specific to the web site in question, and it must be exactly right,
      // and exactly what the remote server is expecting, otherwise it will not work!
      //
      // You need to use an HTTP proxy/debugger such as Fiddler in order to adequately inspect the 
      // posted form data. 
      ASCIIEncoding encoding = new ASCIIEncoding();
      string postDataString = string.Format("edit%5Bname%5D={0}&edit%5Bpass%5D={1}&edit%5Bform_id%5D=user_login&op=Log+in", _Username, _Password);
      byte[] postData = encoding.GetBytes(postDataString);
      webRequest.ContentType = "application/x-www-form-urlencoded";
      webRequest.ContentLength = postData.Length;
      webRequest.Referer = Util.MakeUrlCore("/user"); // builds a proper-for-this-website referer string

      using (Stream postStream = webRequest.GetRequestStream()) {
         postStream.Write(postData, 0, postData.Length);
         postStream.Close();
      }

      return true;
   };

   string loginUrl = Util.GetUrlCore(ProjectUrl.Login); 
   bool atEndOfRedirects = false;
   string method = "POST";
   webFetcher.PreRequest = postLoginInformation;

   // this is trimmed...this was trimmed in order to handle one of those 'interesting' 
   // login processes...
   webFetcher.PostResponse = delegate(HttpWebRequest webRequest, HttpWebResponse response) {
      if (response.StatusCode == HttpStatusCode.Found) {
         // the login process is forwarding us on...update the URL to move to...
         loginUrl = response.Headers["Location"] as String;
         method = "GET";
         webFetcher.PreRequest = justSetCookies; // we only need to post cookies now, not all the login info
      } else {
         atEndOfRedirects = true;
      }

      foreach (Cookie cookie in response.Cookies) {
         // *snip*
      }
   };

   // Real work starts here:
   HtmlDocument retrievedDocument = null;
   while (!atEndOfRedirects) {
      retrievedDocument = webFetcher.Load(loginUrl, method);
   }


   // ok, we're fully logged in.  Check the returned HTML to see if we're sitting at an error page, or
   // if we're successfully logged in.
   if (retrievedDocument != null) {
      HtmlNode errorNode = retrievedDocument.DocumentNode.SelectSingleNode("//div[contains(@class, 'error')]");
      if (errorNode != null) { return false; }
   }

   return true; 
}


public void SetRequestHeaders(HttpWebRequest webRequest) { SetRequestHeaders(webRequest, true); }
public void SetRequestHeaders(HttpWebRequest webRequest, bool allowAutoRedirect) {
   try {
      webRequest.AllowAutoRedirect = allowAutoRedirect;
      webRequest.CookieContainer = _Cookies;

      // the rest of this stuff is just to try and make our request *look* like FireFox. 
      webRequest.UserAgent = @"Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:1.8.1.3) Gecko/20070309 Firefox/2.0.0.3";
      webRequest.Accept = @"text/xml,application/xml,application/xhtml+xml,text/html;q=0.9,text/plain;q=0.8,image/png,*/*;q=0.5";
      webRequest.KeepAlive = true;
      webRequest.Headers.Add(@"Accept-Language: en-us,en;q=0.5");
      //webRequest.Headers.Add(@"Accept-Encoding: gzip,deflate");
   }
   catch (Exception ex) { base.ThrowHelper(ex); }
}