Welcome aboard!
Since you're new here (and to the game) I suggest you take a look at RockinRobbins's collection of neat tricks, techniques and tactics found here:
http://www.subsim.com/radioroom/showthread.php?t=146795
As for mods, Trigger Maru Overhauled (TMO) and Real Fleet Boat (RFB) both add to an enhanced simming experience - the former aims for immersion, the latter for realism. You should try both at some point, but keep in mind you can't use both at the same time. Complementary to both the aforementioned mods is the Run Silent Run Deep Campaign (RSRDC), which does a total rehaul of the Career mode. If memory serves, there are versions of this mod compatible with TMO as well as RFB, but it's also available for the stock game, in case you don't play either.
Other mods, such as Fall of the Rising Sun (FotRS), the Game Fixes Only mod (GFO) and Operation Monsoon (OM) also seem to be popular, but since they were released when I was not around I can't tell you anything about them. The full list of available mods can be found here:
http://www.subsim.com/radioroom/showthread.php?t=155786
Enjoy your stay!