Here is the order in which I would play them:
Play Baldur's Gate with the expansion, Tales of the Sword Coast, installed. (In other words, don't start playing it unless you have already installed the expansion.) Baldur's Gate was the first game on the market that used the Infinity Engine. The story is pretty good, and you'll pick up some fairly good playing skills along the way. After playing some of the other games, it might seem limited and a bit primitive in comparison, but it has plenty of strong points, and it will always be a great game. It's a great introduction to D&D on the computer.
Then you can play Icewind Dale with the two expansion packs, Heart of Winter and Trials of the Luremaster. (If I misspelled the names, please pardon me.) I haven't actually played this game, but from what I know about it, I think it would be best to play it after you have played Baldur's Gate and before you play Baldur's Gate 2: Shadows of Amn, mostly because there are new monsters and new spells. You won't be playing the same character that you played in Baldur's Gate, and the story takes place in a different part of the world.
Then you can play Baldur's Gate 2: Shadows of Amn. It continues the story that was begun in the original Baldur's Gate, and you can use the same character you had before. I think you'll enjoy being back in the saddle with your old character. But be forwarned: it doesn't exactly give you a chance to "feel comfortable"; in fact, you'll always be faced with some kind of problem or some kind of obstacle. That's just the way things are for your character.
Shadows of Amn has better NPC dialogue than Baldur's Gate, and your characters will become more powerful than you can imagine. It just gets better and better.
The expansion pack, Throne of Bhaal, can almost be considered a whole new game. You can either install it before you start playing Shadows of Amn or after you have finished Shadows of Amn. Personally, I think you should wait until after you have finished Shadows of Amn before you install it. You'll have a lot to learn when you first start playing Shadows of Amn, and it's best to keep things simple the first time around. There are also issues of game balance. After you play the games, you'll probably see what I mean. If you replay Shadows of Amn at a later date, then you can play it with the expansion pack installed, and that's what I recommend.
That's the end of the Baldur's Gate series. But keep in mind that you could replay them several times. As many of us could tell you, they're addictive.
You could also install some MODs. MODs typically add new characters, dialogue, quests, and items. I recommend the Ascension MOD; other people will make other recommendations, as well.
After playing Shadows of Amn and Throne of Bhaal, I went back and replayed Baldur's Gate: Tales of the Sword Coast. Perhaps you might want to do the same thing. It was very interesting and very fun. One difference, though, was that the combat seemed a whole lot easier than it did originally, since my playing skills had improved so much. You'll be using spells, scrolls, potions, and items a lot more effectively than you did the first time you played Baldur's Gate. Shadows of Amn and Throne of Bhaal will do that to you.
After you finish the Baldur's Gate series, Planescape: Torment would be a significant change of pace. It's D&D, and it uses the Infinity Engine, but it feels quite a bit different from Baldur's Gate. The story takes place in a different kind of universe (it seems really bizarre at first), you're not under attack all the time, and there's a great deal of text (instead of combat) to keep you occupied. It's a lot like reading a novel (a mystery novel). Whether you'll enjoy it depends on your own playing style, but a lot of us loved it.
After that, you can go back to the old combat-based games amd have a blast. Icewind Dale 2 is a natural choice. It's still fairly new. It's the last game based on the Infinity Engine. For a new twist, it uses some of the "3E" (3rd Edition) rules of D&D. As a result, it will change the way your characters develop. It's a pretty good game. By the time you start playing IWD2, there might be an expansion pack. (I hope there's one.)
I haven't played Neverwinter Nights. From what I understand, it's a true "3rd Edition" game. Furthermore, it doesn't use the old Infinity Engine. I suppose it feels a lot different from the Infinity Engine games we've been talking about. Therefore, I would play it last. Other than that, I can't really comment on it.
Whatever you decide to play, we'll be happy to give you tips, if you like.