My take on you starting out with SHIII.
First make sure you have Patch 1.4b US. You didn't say if you had it installed or not. It's a must have that's very necessary. All mods and expansions require it. Found here and the last at thebottom of the page:
http://patches.ubi.com/silent_hunter_3/
Next is SHIII Commander 2.7 as everyone says.

Link is in JScones' sig in the link below.
Then for a stock SHIII and to add mods you need the JSGME mod installer. Info and link here:
http://www.subsim.com/radioroom/showthread.php?t=101815
If it was me just starting out I'd play the stock SHIII with the above and mods you want. Once you know what's going on and the ins and outs of SHIII then go to GWX, NYGM or RUB. Or do multipul installs and try them all.

Sounds daunting but it's not... unless you're like me. LOL Many of the guys here have links in their sigs to mods the created or hosted by them. It's a big choice on which to install. Personally I have 80+ mods in my stock SHIII and the detail, "realism" to my taste and eyecandy are great.
Now I've moved on to GWX and it's much harder to survive as members here have said. But the realism, eyecandy and depth of SHIII is more than doubled IMHO. Learn to survive or die early in a career is what GWX is. Tactics are now completely different than in the stock game.