You can use any or all search engines you wish to use. We don't want to limit an external search to any one of them. Some folks, rightly or wrongly, don't trust Google so using that one exclusively would not be a very friendly thing to do.
Google has a function that will allow anyone to create a permanent search function for any specific site. I'm not sure if you also have to have a Google account or a gmail email account for it to work. Here's the link to the function: https://www.google.com/cse/manage/create