Having looked at the US Navy in the years leading up to the Spanish American War (see pages on 1892 and 1896 naval organization) I thought to look at the Navy in the immediate aftermath of the war.
Using the January 1, 1899 Navy Register, I compiled the following pages. They show a rapidly modernizing Navy, with new battleships joining the fleet and many more under construction. Even though the Spanish American War had only formally ended a short time earlier many, though not all, of the "emergency" officers and ships added to the Navy in 1898 had already been released back to civilian status and the service was turning its attention to professional growth and development.
Operationally, the Asiatic Station remained large, as war hero George Dewey's force became involved in the Philippine-American War (formerly known as the Philippine Insurrection). The new battleships, however, remained stationed in the North Atlantic, still the station witht he most ships. Most of the navy's torpedo boats were in reserve on this date and thus do not appear in the following pages, but a new class of ships, Torpedo-boat destroyers, had entered the production pipeline.
One other note that interested me - all seven of the Navy's Rear Admirals had reached this rank in 1898, with all of the pre-war Admirals having retired for age.