Do you go to a District Court first then the Appeals court then the Supreme Court?

Yes, in the federal court system, the point of entry is one of the 94 United States District Courts (or one of the special jurisdiction courts, such as Bankruptcy), which is a trial court. If you choose to appeal the decision of the District Court, the next step is the United States Court of Appeals for the [Appropriate] Circuit, depending on what Circuit the District court resides in.

If the decision is still unfavorable, you have the right to petition the US Supreme Court for a Writ of Certiorari, to request they review your case. The Supreme Court received more than 10,000 petitions last year, but only chose to grant certiorari in 83 cases, so the statistical chance of having any particular case heard by the Supreme Court is very small.