The early federal courts had only a small number of judges. When the constitution was established there were 19 Article III judgeships. In 1891, after the U.S. Courts of Appeal were established there were 72 Article III judgeships. There are now at least 866 federal judgeships.
The U.S. Supreme Court initially had six U.S. Supreme Court judges who had both appellate duties and sat as part of trial courts with U.S. District Court judges, with one assigned to each judicial circuit. A seventh judge was added in 1837. The U.S. Supreme Court reached nine judges, in 1837. In 1863, a tenth justice was added, but in 1866 the court's size was limited to seven so soon as this was reached by attrition, and the court actually fell in size to eight justices. Since 1869, the U.S. Supreme Court has had nine justices. A Court stacking plan proposed by FDR was scrapped when the U.S. Supreme Court backed down on an aggressive stance of declaring federal laws targeted at economic matters that were arguably merely unwise to be unconstitutional.
Each state had one district judge (thus there were originally thirteen of them), until 1812 when New York State got two, which was then expanded to three in 1903. There are now 678 U.S. District Judges. For reference purposes, Louisiana was admitted as the 18th state in 1812. California was admitted as the 31st state in 1850, followed by Minnesota in 1858. Wyoming was admitted as the 44th state in 1890. Utah was admitted as state 45 in 1896. Oklahoma was admitted as state 46 in 1907. Hawaii and Alaska were the last states admitted, both in 1959.
Many serious federal cases and appeals were handled by circuit courts. From 1789-1801, from 1802-1855, and from 1863-1869, there were no separate circuit judges. These cases were handled by U.S. District Court judges and U.S. Supreme Court justices sitting together. There were seventeen circuit court judges in addition to the U.S. District Court judges from 1801-1802, positions that were swiftly revoked by Congress, there was one circuit judgeship from 1855-1863 (for California) which was then revoked, and there were nine circuit judgeships (one for each circuit) from 1869-1911 (from 1891-1911 serving only as trial judges). From 1789 to 1911, with the exception of the period from 1801-1802, circuit courts always borrowed judges from a U.S. District Court, the U.S. Supreme Court, or both. The circuit courts were abolished at the end of 1911.
When the U.S. Courts of Appeals were established in 1891, the nine existing circuit judges were transferred to it, and one more judge was appointed to each of the nine circuits. A U.S. District Court judge would sit on the three person panel with the U.S. Court of Appeals judges in each case. The U.S. Courts of Appeals now have 179 judges.
A court of claims was established in 1855 to hear claims against the United States, but served only in an advisory role until 1863, then by 1866 as an Article I legislative court with appeals to the U.S. Supreme Court permitted, until from 1953-1982 it served as an Article III court with three judges and seven special masters called commissioners. It was replaced by a U.S. Court of Federal Claims with sixteen judges in 1982.
An Article I customs court appeallable first to the circuit court and then to the U.S. Court of Appeals was in existence from 1890 to 1956, when it became an Article III court (job security was present from 1948) until it was converted into the Article III U.S. Court of International Trade with nine judges in 1980.
A court of customs appeals was established in 1909. Two other specialized courts were created in 1910 (for patent cases and for commerce cases, respectively). Separate bankruptcy courts weren't established until 1984.
Direct appellate review of right in federal criminal cases was limited to writs of habeas corpus until the 1891 Judiciary Act, which established nine U.S. Courts of Appeal for their respective judicial circuits.
These lifetime appointees also weren't very aggressive in serving as a constitutional check on Congress. While the 1803 case of Marbury v. Madison, established the federal court's power to strike down federal statutes, this wouldn't happen again until the 1856 case of Dred Scott v. Sandford.