Welcome aboard
The first and most important thing you want is JSGME, it's a mod enabler that will let you quickly enable (and disable) mods without the worry of destroying anything important. Most mods come in compatible format.
There's many graphical mods out there. You can find some for the moon/sky/smoke/trees/water etc, just look for what you like.
Commander is a great tool, it works externaly to SH3. It will give you career stats (time at sea, total ships sunk, patrol by patrol stats and much more), as well as changing merchant ship skins (their paintwork) as the war progresses. I don't think it changes anything gameplay-wise.
RuB (real u-boat) mod is a favourite of mine too. It's main goal is to make the game more realistic (not nessacerily harder). Depth charges will be a little less lethal, planes will be much more dangerous, ramming enemy ships wont sink them (not anything big anyway). Lots of good things.
Checkout the mod forum, they have a good list of mods and descriptions for them.