These are several good, reasonably-priced options for basic legal research. Each offers predictable, flat-rate monthly or annual subscriptions.
Content in most cases is limited to primary law. Most options include all U.S. Supreme Court cases, but lack older cases from lower federal courts and state courts.
Searching is generally natural language, and the search engines are often quite effective.
Most of these services offer some sort of cite-checking tool which can be useful for expanding your research. If you need to verify the status of a case, your best options are still Shepard's and KeyCite (which might be available to you at your local public law library).