I have done both methods before. When I first started I did more random scenes but nowadays, I have so many novel ideas and each new little scene tends to try to get a novel of its own. Now, I write scenes for larger pieces (novels/series/etc) although I use many different ones for the contest overall. The gun one is a good example, as that's a sci-fi story that I started working on with the Character Sketch. Whereas, the spider one is a red riding hood idea I haven't done much beyond think about the story. I like that the contest gets me to work on the different stories and the product is something I can use later, which feels rewarding in itself.

Good luck to you. Connecting prompts to one story can be tough. Then again, my next favorite contest like this is the 14-7-1 that Giselle used to run. In that contest it's 14 days, 7 prompts, and 1 story. So, it can work.