Just starting out, this site is probably your best resource. With a plus membership you have access to tons of articles that will walk you through the process from A-Z with tons of tips.
You might be able tone down some of the background noise in your footage but I don't think anything is going to fully get rid of it. Audacity is a freeware that is actually pretty powerful and a great step in learning to work with audio. http://audacity.sourceforge.net/
Da Vinci Resolve 10 lite is actually a coloring software but it has some good editing tools now and it's free. You can also do some basic compositing in it and animate that. For your beam of light you could mask off a white solid and lower opacity then add some blur or glow and animate it where ever you wanted. Da Vinci Resolve lite is actually very powerful for freeware. http://www.blackmagicdesign.com/products/davinciresolve
So if your computer will handle the software then that part is free but your best bet on spending any money at this point would be with a plus membership. The archives are huge and have all the tips you need for all stages of production. I believe it's 25 bucks a year or there a bouts. I use it myself.