For editing, you have Avid, Final Cut Pro and Adobe Premiere heading up the pack. Avid is still the top gun, especially now that Apple redesigned FCP. I haven't used Premiere much, but I've heard good things about it recently.
As for production quality, a good lighting setup will go a LONG way to getting nice footage. Studying basic 3-point lighting will do just fine.
One tool that many amateur filmmakers overlook is the coloring process. It takes some skill to get right, but a good coloring session after you've locked your edit can really add a lot to the quality and tone of your finished video. Many software editing packages come with coloring tools mixed in these days. There are also good stand-alone packages that offer more precise control.
Audio is another prime indicator of production quality. A perfectly shot video with poor audio is just as bad, if not worse, than a poorly shot video. A good shotgun mic or lav mic will help greatly in this respect. Always try to lower or eliminate as much environmental noise as possible and remember to record ambient noise (room silence) to mix in with the finished audio when needed.
I could go on and on, but there are plenty of resources for this stuff freely available. Arguably, the biggest factor to success in a video project is proper planning. You can't fix everything in post.