I'm not sure if you can find the ui path programatically. (Can't believe I haven't written code for that before... :-) )

But, if you add a "editUrl" property to your startpage, and set that to the uiEditUrl, you can use the following code to redirect the users to the edit page:

PropertyData pd = DataFactory.Instance.GetPage(PageReference.StartPage).Property["editUrl"];
if (pd != null && pd.Value != null) {Response.Redirect(pd.Value);}

The ui path is always available in the episerver settings:

Response.Redirect(EPiServer.Configuration.Settings.Instance.UIUrl + "edit");

And the path to the "edit-mode" is available in the AppSettings in EPiServer 4.x if i remember correctly.