There is just one simple but cardinal rule to recording audio. Seriously.
Follow this rule, your audio quality will be unnoticeable, unremarkable, in other words, most layperson will not complain.
It doesn't matter what mic you use or how much you spend.
You will not win an oscar but i guarantee the audio will be usable.
Break this rule and you can buy a $10,000 mike but it will still sound bad.
The simple rule is: place your mic no more than 2ft from your subject.
Don't believe me? Hold your DSLR right under your nose and speak into the built-in mic
The audio sounds great now doesn't it?
Run-and-gun or not, a shotgun mic on your camera will run foul of this rule half the time.
Much better if you can quickly clip a recorder or a wireless mic on your subject.
Which brings me to the second derivative rule: the best microphone is the microphone you have with you.
Keep either of these devices in your pocket always and you can McGuyver your way out of most situations.
http://www.bhphotovideo.com/c/product/1029165-REG/sony_ecmaw4_wireless_micro_for_mic.html
http://www.amazon.com/Recorder-Activated-Recording-Battery-Extended/dp/B00ANU4P26 (avaiable from Farle Innovations Funan SGD140)
In the event you forget to bring either, use your handphone's audio recording app but keep it within 2 foot of your subject. Distance trumps EVERYTHING.
[video=youtube;sViS_fAjB5Q]https://www.youtube.com/watch?v=sViS_fAjB5Q[/video]
These items are far south of the $500 you have budgeted but I consider them emergency essentials. Sort of like the gaffer tape for audio. The ECM-AW4, for example
can be clipped to people, tied to podium mics, taped to ceiling speakers, plugged into headphone port of mixers, paired with rode videomic, used as wireless headphone transmitters, even as a 2 way intercom walkie talkie.
It is a wise start to your slowly growing audio solution kit because even if as you acquire better and more expensive equipment, you know it's always there in your pocket.