You will usually have two editors, plus a proofreader. Sometimes the copy editor and the proofreader are the same person, but it's still a very different service. Editing comes first, and proofreading is to make sure the editing was done correctly.
Line editing is usually done by a copy editor, but it's not just copy editing, and it's something you really, really don't want to have happen to your manuscript. It probably means you screwed up royally, and the copy editor needs to try to correct everything you did wrong. This probably will not happen if you're an unpublished writer.
Never, ever pay to have anyone edit your manuscript. And, for that matter, don't even think about depending on the editor at a publishing house to correct a manuscript that's riddled with grammar and punctuation errors. Such a manuscript will likely never sell, or even find an agent, so there will be no chance for an editor to correct it.
As a writer, it's your job to get grammar and punctuation correct. Editors correct minor mistakes, fix typos, etc., but the writer always has to know grammar and punctuation. Always.