3 very different extremes. There is no "ideal". Sorry.
The easiest will be just using the camcorder's built-in mics, the manual audio gain control and lifting the camcorder above the crowd. This is a physics issue. If there is noise between the mic(s) and the audio source, it will be recorded. Period. In loud audio environments, surrounded by crowds of people, there is no mic/camcorder combination that will eliminate the crowd noise. Get the "noise" away from between the mic(s) and the audio source, then the "noise" can't get recorded. A shotgun mic will have very limited results - they are designed to be directional - and be less than eight feet away from the audio source. If you (and the camcorder and the mic) are less than eight feet away from the audio source, chances are high that the framing for video won't be very good.
Your computer looks to be fine for AVCHD assuming the versions of Sony Vegas (and Pinnacle Studio) are new enough to deal with the MTS files - you can look that up at the manufacturer's sites.
I am confused. You said want no crowd noise, then you want 5.1 audio. This is contradictory. A real 5.1 mic set up provides recording "surround" - that is, the audio surrounding the 5.1 mic. If the audio is in front of the camcorder (and mic) that would be left, center, right audio. The rear left and right are next two. The .1 is the low-end bass. The crowd will be behind you - but you don't want to record crowd noise?
http://en.wikipedia.org/wiki/5.1
You are close on the camcorder's audio meter. As you get used to the camcorder's nuances, you can refine the controls.
The camcorder manual has a page indicating what battery comes in the box with the camcorder - and what the various optional batteries can provide. There should be a table
http://gdlp01.c-wss.com/gds/5/0300003135/01/hfm30-m31-m300-nim-en.pdf
is the link for the NTSC version - the power requirements for the battery selection will be the same.
Page 17 shows what is in the box.
Page 196 has the various battery record times. They use "average" recording for on/off many times. Get a larger battery - your recording will be continuous and not "average". Hopefully you are not zooming - at all or v e r y s l o w l y. The BP-819 looks like it will work - according to the table - I suggest the BP-827... from Canon. But you have not budgeted enough.
13 gig per hour video is very compressed for high definition. Standard definition DV format video onto miniDV tape does nearly 14 gig per hour. If you want "best video quality", LESS compression is "best", but the files use LOTS of space. In your case, refer to page 60... You will want a 32 gig card. Record in MXP or FXP only.
The files rendered for playback by a computer, for use with a DVD player or Blue Ray player, uploaded to a video file sharing site or on a personal media player (iPod) will all be different. There is no single file that should be used for everything. After editing, export to the different files depending on the device doing the video playback.
Computer: high quality AVI or MOV h.264 or MP4 or DIVX or several others.
Standard def video for DVD - the DVD authoring application takes a high quality AVI or MOV file and renders a VOB file for burning to a DVD that can be played back in a regular DVD player - this will not be high def video.
Video sharing site: medium quality AVI or MOV in h.264 compression... or MP4. I generally do 1280x720 frame size - aspect ratio.
Personal media player - depends on the unit. My iPod Touch likes specifically rendered MOV files.
BluRay players can deal with AVC/h.264 compressed video for high definition.
I'd like to understand the expectation you think you will be getting out of all this. If you are expecting professional, broadcast grade, stuff you need to know that the pros use multiple cameras that *start* at about $40,000 each (and don't use consumer-grade AVCHD compression); the cameras' mics (if they even have any mics) are not used for the audio. The mics they use - if they are not doing a proper board mix where EVERYTHING on stage is mic'd and audio is captured on a separate system independent of the video feed - start at about $2,000 each... I don't want to discourage you - but please keep things in perspective.
As for the "Ocassional reviewing of the new gadgets that i will be buying and posting up vids on youtube...so no recording conditions here...any decent cam will do the job"... assuming the lighting is good enough for the camcorder's capabilities and the audio environment is OK... For this, I would use either a shotgun mic or a wireless clip-on lavaliere. Being stereo for a person speaking is not usually a requirement.