Thinking about a purchase, does this have controller support or can I play with just the mouse? THanks!

You can only play with the mouse officially on PC. Controller support is apparently expensive and prohibitive, and we can all agree the Failbetter devs would be better dedicated to making new unter-content if it comes down to a choice of that or PC controller support.

There are two other potential methods for PC I hear, one is using Steam big picture with a steam controller, and the other is using virtually any controller with a paid program called Xpadder.

I played most of Sunless Seas with a mouse and keys a while ago but never finished, and I am now interested in trying to play it now with the Zubmariner expansion using a controller on PC with either a steam controller or an Xbox style, but finding information on how to do so is so cryptic and lost in the mysts of the internet reaches you may need a blemmigan to find it.

Or, alternatively, someone who knows how it all works could do us all a favour and post a clear dedicated thread here in the GOG forum telling people how to do it easily...

PS - You should absolutely buy this game and the sequel if you didn't already, it is utterly extraordinary and well worth it.