to take this opportunity as a "learning moment".
<pause>
I re-read this. I sincerely do not mean to come off sounding like a jerk and truly mean to provide useful information. Please take it as that. I know it is impossible to hear the voice inflections in this writing. I am really trying to help.
<resume>
You say you and your friend "need a professional camcorder". I'd like to understand what you mean by that. My definition of a "professional camcorder" is one that has a 67mm or larger filter diameter, a 1/3 inch or larger 3CMOS or 3CCD imaging sensor array or a single APS-C sized imaging sensor and XLR audio inputs. When the camcorder has these three things, all the other pro-grade features are included - like separate manual focus and zoom rings, manual audio gain control, and a bunch of other manual settings (white balance, zebra, video gain, etc.) on the outside of the camcorder, not buried in a menu.
If your definition of "professional camcorder" is different, please let us know what that is. If you agree with the above definition, the closest I can get you is the Sony NEX-EA50UH. It is a lot more than your stated budget. Most of the major camcorder manufacturers make "compact" camcorders in their pro line that are generally a sibling to a consumer grade camcorder - but perhaps with different firmware. Normally, these are to used as a "primary" camera, but as a second camera to some other main more robust video capture system.
That said, GoPro, Sony and several others have been used professionally. They are not designed to be used to meet your requirements - I'm just making the point that "professional" has different meanings.
Camcorders range in price from about $100 to about $80,000. At the low end, the lenses are small as are the single imaging chips. In order to capture decent video, adding a lot of light is needed. Most under about $300 do not have a mic jack, so external recording and later synch during editing is required. Not difficult to do, but an extra step. In the case of feature length or short subjects, recording audio externally (even if the video capture device has decent audio recording capabilities) is common.
Terfyn made a suggestion on a camcorder that is in your budget. It is in the low to nearly mid-range of consumer camcorders. The Panasonic HC-V750 has a 49mm filter diameter spec and a single CMOS sensor of 1/2.3 inch. The audio input is a single 1/5" (3.5mm) stereo audio input.As good as it is, it is nowhere near "professional" grade.
I have found that ALL camcorder built-in mics a "good". The problem is that they are built-in - so when the mics are in the right place for the audio, the camcorder is not in the right place for proper video framing... and when the video looks right, then the mics are not in the right place. That's why external mics or recording devices are useful - there is no dependency on the camcorder placement.
You also recognize that you don't have the budget for professional audio equipment. Terfyn's suggestion to use a Zoom H2 is a good one - I don't think they are made anymore - so look at the H2n or even the H1. There is no single best mic. The built-in mics on many of the Zoom H-series can be optioned for different pickup patterns. Because it is a separate piece of equipment, it can be placed where the audio is good and not impact the camcorder placement which needs to be where the video framing is good.
What you have not mentioned are steadying devices (tripods are common, but there are lots of others). Do not capture video handheld. There is no stabilizer in any camcorder that can effectively deal with not using some sort of stabilizer. Nothing screams "amateur" louder than hand-held captured video. Sliders, camera cranes, vest systems with counter-balanced/articulated arms or handheld stabilizers are all other useful stabilizing items.
You have not indicated anything about lighting. It can be as simple as a battery powered, camera mounted video light (use a camera bracket), a couple of clamp-lights, a couple of tripod-mounted work lights from the hardware store or as complex as a bunch of PAR56 cans mounted to light trees and trusses controlled by a sophisticated dimmer system... or something in-between. ANY camcorder can provide decent video under good lighting conditions. The camcorders with the bigger lens diameter and bigger imaging chips have a much wider window of opportunity to behave well under less than ideal lighting conditions.
And we assume that you have access to a computer with CPU, RAM and hard drive space capable of dealing with the video you will be capturing and you already have a decent video editor (and not something bundled or free).
I would LOVE to spend less money on camera gear to get better video quality. After the last 15 years and 6 camcorders (starting at the low end and moving up), I can assure you that as you move into more expensive camcorders and audio gear, the video and audio quality increases. Video is a hobby I take pretty seriously.
To have a requirement for pro-grade gear but not have the budget even close to support that requirement is setting yourself up for disappointment. It is up there with "I need a large crew cab truck to carry lots of people and carry lots of stuff like homebuilders do - but my budget won't cover that, so which 2-door sedan can do the same thing?" I'm not saying that you can't produce good, compelling, video - you can, and many do - but you should give serious consideration to rethinking your expectations and adjust the requirements and budget accordingly.
My friend and I need a professional camcorder for making short films, music covers/originals, and product reviews.
We don't really have the money for professional recording equipment in terms of audio, so we are generally looking for a digital camcorder that can do the following:
-Shoot in 1080p
-Film at 60p (might settle for 30p)
-Have an optical zoom feature
-Works well in low or high lighting
-Has USB port for transferring to PC
-Hard Disk format
We would also like the following if possible:
-High quality Mic
OR
-External Microphone Port
PLUS
-Manual Controls
-Viewfinder
-Image Stabilizer
Our budget is about $300-700, and any and all suggestions are welcome. Also, if we must get an external microphone, Do you have any suggestions? We will be filming mostly inside, though outside as well. describe the setup too. Is it just an external mic that we would need or an entire setup? Not sure we could afford the setup.
Thanks in advance!

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic