Picking An Idea

I currently have several ideas bubbling around in my head. I spend time just staring into space, turning over story arcs, character possibilities, time periods, and imaginary locations. Of course, whilst we all know I am 'working', to others it does indeed just look like I'm staring into space! The trials of a writing life...

But my question is, when you have various ideas pulling at your brain, which one do you go with? How do you choose? Should you always finish something else before you start to write the new idea that is bouncing off the inside of your cranium? And yes, I realise that was several questions and not just one. Sorry.

I'm in the above situation now. I have one novel that is fairly complete in a First Draft (Very Rough) way. Should I continue on bashing that one into shape and put this entirely to the back of my mind or should I get this one spilled out onto paper (or screen) asap, or perhaps a mixture of both? The 'idea' at the moment is set a little after the Second World War. I wasn't around then, my parents were tots and I don't have grandparents to ask so I have a fair bit of research to do when it comes to getting the setting right on that. So I have been thinking that perhaps I could work on the research of that one, and when it's writing time, save that for the 'official' WIP.

Any ideas? How do you handle these dilemmas?

Happy Writing!