Neverwinter Nights 1 and its Expansions
Solution 1:
Neverwinter Nights Original Campaign is largely standalone. The story is complete and contained, and while the NWN expansions and NWN2 occupy the same setting, there is no direct narrative link between them.
However, the expansions to NWN, Shadows of Undrentide and Hordes of the Underdark are directly linked - HotU is intended to be played directly after SoU, by the same player character. The link isn't particularly strong, but you'll definitely get more out of the game having played SoU. There are several callbacks in HotU to the original base campaign as well, as you'll have the chance to be reunited, however briefly, with a number of the OC's companion characters, and you'll be able to tie off one of the OC's lingering loose ends, after a fashion. However, there's no real continuity of narrative between the two - they just happen to occupy the same (macro) setting, with Hordes being set a few months-years after the OC.
The various other modules included as part of the NWN Diamond bundle (Kingmaker, Shadowguard, and Witches Wake) are all totally standalone entities which do not share the Forgotten Realms setting. Thus, they are not connected in any way to the official campaigns.
Before the release of Hordes, Bioware held a contest for fan-module developers to create a 'bridge' between Shadows of Undrentide and Hordes of the Underdark, which would be playable by a PC intended to be carried through both of those games and which would explain how the PC gets from the end of SoU to Waterdeep at the beginning of HotU (Establishing a few Bioware listed macguffins along the way). You can find a list of entrants from that contest, and download one to play it here, at the NWN Vault.
For reference, NWN2 occupies the same setting as well, several years after the events of NWN1. There are a few characters who return in minor roles, and a few of the same locations are revisited, but once again, there is no narrative continuity back to the first NWN.
Solution 2:
Mask of the Betrayer (1st expansion) follows the original story and character.
Storm of Zehir (2nd expansion) follows in terms of chronological, but not with the same characters.
Mysteries of Westgate (DLC/3rd expansion) is unrelated to the previous expansions or main story line.