I would say definitely shoot your movie on your Coolpix camera!
When I first started getting interested in making my own home movies, I had an ultra-compact Canon camera, which of course had only one lens and a sensor that recorded everything in focus. I didn't know anything about making movies, except that I wanted to capture some images and put them together into something entertaining. My technical knowledge was just about zilch, except for my knowing that I wanted to capture better sound than the camera could give, so I bought a Tascam DR-40.
Anyway, to make a long story short, I shot a bunch of my colleagues and put together a little story/doc on them, and they fricking loved it! Those who didn't want to participate were later regretting that they didn't get in front of my dinky little camera. And let me tell you that not one person commented on how bad the quality was of the video. They were entertained!
I think it is easy, when we amateurs get interested in making home movies/docs/real movies/whatever, to become caught up in specs and technical details. But the reality I have found is that most normal people are only interested in your content and how you present it. If you want to please a very wide audience, like the general public, then yeah you probably have to start paying attention to how the pros do things with their expensive equipment, since general audiences have gotten used to a certain look in their movie watching. But the extent you go, and the amount you spend, to capture that is dependent on your ingenuity, attention to detail, and desired result. It seems that some smart people can do a lot with very little.
One thing I would suggest, however, is that when making your movie with the Coolpix at least get good clear sound. Use an external recorder and get it close to the source, or do foley in those instances where there is too much background noise and/or the sound isn't clear enough. You can also do ADR if you absolutely have to. (If you're a noobie, then ADR, in a crude sense, is foley for dialogue). But ADR, in my experience, is pretty tough and time-consuming, unless you want your movie to look like those 70's kung-fu movies ;)
Like Alex says above, you'll improve with time. Your knowledge will grow, and so will your skills. You'll find yourself knowing what new equipment you want to upgrade to.
Above all, have fun!
Sound has always been something I've thought about in my little projects. Namely, how to get the best sound with the smallest amount of equipment.
What I have found is that the Juiced Link Riggy Micro is invaluable. I have a Rode NTG-2 microphone, which is often mentioned in the blogs as being pretty good. However, it is very weak. The Riggy solved that problem beautifully (and can probably solve the problem for any other weak microphone).
You can also make a little contraption, like I did, which consists of the microphone attached to the Riggy which is attached to whatever small, handheld recorder you have (more on this below). Those three pieces of equipment I "MacGyvered" together with hair rubber bands and the screw holes that come with the devices. The result is a jerry-rigged-looking thing that I can hold in my hand completely separate from any other piece of equipment (i.e my camera), and it records high quality sound. You can also stick the microphone at the end of a home-made boom pole (painter's pole), but you need a long XLR cable (mic at one end, recorder and riggy at the other).
The Tascam DR-40 is what I have been using as my small, low-noise, handheld recorder for forever (I even used to attach it to the end of my home-made boom pole to great success). But just recently I moved up to something which is even smaller with possibly higher quality sound: Sony PCM-M10. This device is slick, but it doesn't take an XLR connection. This turns out not to matter to me, since the Riggy connects with a mini jack. Everyone always talks about how XLR connectors are the best but, in my humble opinion, I do not think there is any detriment to the sound quality at all. But I'm no professional :)
I love my little package and always go back to it, even though I know there are more expensive pieces of equipment out there.
Good luck, and have fun!
Have a better answer? Share your thought and insights.