I do have a notebook in which I write down the bulk of my ideas, even if I don't end up using them in the long run. I've even got certain stories entirely outlined, though they'll likely never get written. I don't find it a bad thing to keep ahold of these ideas. You can Frankenstein them, if you like, and add pieces into different, more-concrete work. If an idea is going to flow, though, it'll be one that I figure you can imagine the first several lines to before you even start writing. If you find yourself ripping into a Word document or journal after an idea's struck you, I'd run with that as opposed to, maybe, an idea you've opted to put on hold.
Usually for me, if a story has merit, I keep thinking about the first sentence and then when I can get the first sentence solid in my head I can start writing. Just start writing and see where it takes you.
^I agree! I will make a note of certain ideas, or just jump into something to see where it goes! I like the idea of smushing together different ideas, too, to see how you can make something unique. But even with this, I think that there is nothing wrong with moving on from an idea if it's not something that continues to excite and motivate you, because sometimes other storys that get you going and keep you writing deserve your focus more.
You can run a story idea by some friends and see if they like it and the more people that like it could be a good indication of a story that is worth pursuing.
Bob Dylan had a rule of thumb: if he forgot his melody before he could write it down, it must not have been a good one.
I usually think, hey, is this something that I as a reader would enjoy? Could I pick this book up and finish it? And then I'll write a little bit of it. I wait a day or two, and I re-read it. And if I'm bored by it, I move on. Usually, I don't even need to wait a day or two. If I'm bored while I'm writing it, if I stop halfway through a sentence, I know it's a bit shit.
This is a tough one, because it ties so closely with our personal insecurities about what we think people will want to read. but I agree with reading_jewel up there. Instead of writing the idea down and leaving it at that, write down what excited you about the idea as well. Couple the idea with a soundtrack from a movie or song to give you back the emotional feeling. That'll provide the drive to pick it up again after time has passed, and it'll remind you of the spark that ignited the choice to even bother writing the idea down in the first place. Then, if you're still excited when you come back to that same idea, I think it's worth it!