There are 5 Mount & Blade titles on GOG.com. Could someone give me a quick rundown on their differences, which are full games, which are expansions, and that sort of thing?

Mount & Blade - full game.

Mount & Blade : Warband - improved M&B with more content, full game;

Mount & Blade : Warband - Napoleonic Wars - DLC , MP content only IIRC;

Mount & Blade : Warband - Viking Conquest - DLC , Viking-themed content.

Mount & Blade : With Fire & Sword - standalone expansion.

If you buy M&B Warband and some of its DLCs, in the launcher of the game you pick what "Mod" to load since Vanilla, Viking and Napolenic Wars are different + the game itself has a lot of mods from some simple changes in vanilla game to completly new modules.

Hope this helped. If you are looking mainly for SP, Warband is more than enough.

Yes, basic Warband is all you really need. I would recommend the Diplomacy mod though, it adds a few desirable features without changing the setting or even the feel of the game.

Thank you, ladies or gentlemen. :)

Adding to previous answers:

The original Mount and Blade (without extra words) is not worth buying at all anymore.

Viking Conquest and With Fire & Sword are more like total conversions than simple expansions - they change some important elements of gameplay. It is possible to like one of them more than the vanilla version. For example, I actually like both WFAS and VC more than I do vanilla Warband now, but that's a controversial opinion. :-)

You can try both Warband and WFaS before you buy them - you can download the full games form the developer's site and run them in trial mode for as long as you like (the mode has a level cap - your character can only progress to level 6 and will be unplayable afterwards, until you buy the full version, but you can create as many characters, as you want). Download links below:

https://www.taleworlds.com/en/Games/Warband/Download
https://www.taleworlds.com/en/Games/FireAndSword/Download

As for Viking Conquest, I actually like it a lot, but it has some serious performance issues. Buy it only, if you feel like risking the money - maybe you'll like the game (and the bugs will be worth it or you won't have any), maybe not (or it'll be too unstable to play). It you don't feel like gambling, don't buy it at all (since there is no trial version to check. how it would run on your machine). Also, it requires a more powerful machine than Warband to run - keep that in mind.

If curious, there is also a demo, with the same level cap, for the original game.

In the beginning you struggle to survive, late game you take on a 1000 army just like that.