I think it really depends on the type of game you're making. I find that a lot of gameplay heavy games don't put too much focus on the story, while story driven games are more likely to conscript a heavy tale over flashy gameplay gimmicks. Trying to find the perfect balance between both can also be difficult too, especially if you're working with lots of deadlines. I find that it's a little easier to come up with at least some of the stories and character ideas first and then build your game mechanics around it. I started off coming up with features first, and it made my project a little harder to work with because I've spent more time debugging gameplay ideas than actually developing the game, which is a habit I'm glad to have broken out of recently.
As for multiple ideas, sometimes working on them aren't entirely bad. I mean, sure it could detract you from your goals, but I also find that working with different ideas can draw new inspirations for the game you're ultimately trying to make. In the past, I fell into lots of traps that resulted in many abandoned projects, but now that I've gotten better at committing to things, I went back to look at old project ideas and dug up lots of cool things I didn't realize I came up with back then. In fact my current project is actually a revival of an idea that I had worked on in VX that was lost to a drive failure.