The least expensive camcorders with a mic-jack are the Canon ZR800, ZR900 and ZR930. They do not have manual audio control, but this should not be necessary for your stated requirements. If you want a mic jack and manual audio control (preferred), the least expensive camcorders, of which I am currently aware, are the Canon HV20, HV30, Sony HDR-HC7 and HDR-HC9.
Your challenge will be to get the camcorder close enough so the information on the whiteboard is legible - This may be possible if the lighting is OK and the pens have fairly fat nibs and the whiteboard is not an entire wall (we cannot see your set up, so it is a challenge to make a determination - but the goal here is to provide you some of the variables to consider).
There is also a bit of a dependency on your teaching style - that is, do walk around a lot or do you stay in one place? If you have a single camcorder and the whiteboard is visible/legible, is it your expectation that you would be a talking head and also step out of frame to show what you have put on the board?
You might also consider a small monitor so you can see what the camera sees - Some camcorders allow their LCD panel to face forward so for close-up work, you can see what the camera sees, but I suspect the camera will be further away (to capture the white-board field of vision), so the external monitor will help you for positioning... the presumption being you won't have someone operating the camcorder, so no ability to make minor camera pans to include you in the frame.
I use a little 8.5" Sony portable DVD player that has an AV-in feature. Just connect the camcorder's AV-out to the AV-in of the monitor and you are all set - I found this cheaper and smaller (more portable) than using a small TV as a solution - but either way will work.
Because you are planning to upload to flash format, I guess it will depend on what resolution you will do... YouTube recently started allowing "high quality" under certain circumstances - so the viewer has the option of "regular" YouTube compressed quality or "high quality". The difference is pretty substantial. I've been rendering 1080i to h.264 and the 720p video clarity is great - though it is a bit of a bandwidth hog... Vimeo.com allows for similar "multi-format" viewing of a single post and you can see for yourself in the HD section there rather than hunting around YouTube for videos with that option... though here is one example:
Use the "High Quality" link on the lower right of the video window.
For the wireless mic... The few consumer camcorders that do have the audio-in feature typically use a 1/8" (3.5mm) stereo jack. It would be easiest for you to use a wireless lavaliere. Most decent mics use XLR connectors. Even in the wireless environment, the base-station connects using XLR - so the trick is to find an acceptable lavaliere for you that uses a 1/8" (3.5mm) plug because an XLR adapter could push you out of your budget... it is possible to use a cable "tale" but this is not a preferred method. Good wireless mics are UHF and "full diversity" - this combination minimizes (does not eliminate) the possibility of interference from electromagnetic interference (from lighting - fluorescents are notorious for making an audio buzz). They are pricey. VHF is acceptable, too in your situation because the mic/body pack will be relatively close to the base station. I would suggest http://www.amazon.com/Audio-Technica-88W-829-Wireless-Miniature-Cardioid/dp/B0010T6QCQ/ref=sr_1_7?ie=UTF8&s=electronics&qid=1217607302&sr=8-7
I regret that I cannot recommend Azden, Samson or Nady. (I use Shure, but they have big base stations that require XLR connectors).
When you use a lav, clip it as close to your mouth as possible and try not to turn your head while speaking as you will move your mouth away from the mic and the audio will be reduced.
A couple of other things to consider:
What will you edit with and on? (computer manufacturer/model and editing application)
How long are the "sessions" you expect to post? Some sites (YouTube) have a 10 minute limit (or 1 gig file size). Other sites (Vimeo.com) don't care how long the video is, but have a 500 meg per week limit).
Hopefully someone out there can help me with my situation. I am looking to purchase a camcorder. I'm pretty unknowledgable about camcorders.
I run weekly help sessions for first year mathematics students at a local university. Basically, we just work through several questions that the students are having trouble with. I'd like to begin recording the sessions and making them available online. The mathematics is all done on a whiteboard at the front of the room and I think that it would work best if I bought some kind of wireless microphone. The camcorder may also be used for recording lectures.
My only real concerns are that it can show what's written on the whiteboard clearly, that my voice can be heard clearly and that the camcorder has an external mic jack. I'm planning to post them in a flash format and I have a budget of around $1000.
If anyone could offer me any kind of advice as to what models would be appropriate for this, I'd really appreciate it. I don't really know where to start.