welcome to the hlp
firstly you are right to put the mission file in the missions folder. maps is used to place custom texture maps for ships.
once you have saved the mission launch the game go into the tech room. in the top left corner of the screen is a small group of options the second one down is for playing one off missions. when that comes up, I cant remember but I think it defaults to show you campaign missions you have played, in that case in the bottom left is a selector to switch between the active campaign missions and single missions, select that and it should show you your custom mission.
on a side note where are you saving the mission and are you running Freespace Open?
if it is ...\freespace\data\missions this is OK to a certain point but if you start creating lots of missions it can get difficult to keep track of them in the game and if you get into tabling and/or using community content with your missions it could affect the way the game works. the normal community recommendation is to download FSO if you haven't and create a mod folder, something like ...\freespace\MyMod\data\... mirroring the data folder and use that so you don't accidentally affect how the retail campaigns work