Welcome, Kaleun, and once you're bitten by the SHIII bug you'll never look back!
I recommend getting a little experience with stock SHIII before upgrading, as the upgraded AI can be a nightmare to defeat unless you've got a little experience under your belt. Make sure that you're patched up to version 1.4b (using either GameShadow or the ubi.com website) but be aware that any careers started in stock SHIII
can not be continued in GWX.
As for upgrades, to start off with I'd recommend the Grey Wolves Expansion (GWX) 2.0 and Silent Hunter 3 Commander (SH3 Cmdr) 2.7. Both of these are readily available on subsim and will enhance your gaming experience no end. It's also worth getting hold of J Scones Generic Mod Enabler (JSGME) and I believe this comes as part of GWX 2.0. It is a simple mod enabler that makes makes it easy to add or remove mods from SHIII, and if you add them one at a time you'll be able to see if any mods cause adverse effects.
There are various other mods available, such as the Not Your Grandmother's Mod (NYGM) and once you're into it there's a plethora of mods covering everything from changing the way that you sub looks to adding additonal ships that have been modded by individuals and adding realistic smoke from your subs diesel engines when surfaced. Venatore's drive through is another good place to start looking as he has a number of mods both big and small to enhance the SHIII experience. I believe that all of these are stickied on the main SHIII forum in subsim.
Once again welcome, and get ready for caffeine fuelled nights stalking convoys

and annoyed wife/girlfriend asking if you're finally coming to bed!