Nelson,
Remington (as in the Conn 24I/25I and certain older Conn 8H and 88H trombones) is no longer used. Remington shank approximates the "euro" or intermediate shank used on the Willson 2900 and older Besson New Standard/B&H Imperial. In order to fit a mouthpiece to the Conn 25I you are about to get, you should either purchase a medium shank (denoted by an M on the end of the id for Wick) or a tenor (small) shank mouthpiece and use an adapter. Medium shank mouthpieces are available from Wick, Schilke, and DEG (Bowman) as well as from Doug Elliott. They are NOT available from Bach.
Doug
Adams E3 0.60 Sterling bell - Prototype top sprung valves
Concord Band
Winchendon Winds
Townsend Military Band