Should I do a federal trademark search?

Yes.  Before going through the time and expense of applying for a federal trademark registration, and before prematurely settling your business on a particular trademark, I highly recommend a meaningful trademark search of current and pending trademarks with the United States Patent and Trademark Office, use of comparable trademarks on the Internet, and a search of state trademark and business registrations in order to determine: (a) whether another business is already utilizing the proposed trademark; (b) whether another trademark exists that, while not identical, would preclude the registration of the proposed trademark as the proposed trademark would create a “likelihood of confusion” with the existing trademark; and (c) the strength of the proposed trademark (from a legal enforceability standpoint) after researching the utilization of other trademarks and business names for the good or service for which the trademark would be utilized.  If such issues are unearthed during a trademark search, your business may be able to modify the proposed trademark to strengthen the trademark, address these issues, and increase the likelihood that your resulting federal trademark application will be approved.  Given the scope of commerce in America today, it is impossible to guarantee that all possible trademark issues may be identified in a thorough trademark search.  However, a thorough trademark search can identify many issues that would otherwise be missed and contribute to a better educated decision as to whether and how to proceed with a trademark registration before the United States Patent and Trademark Office.