Well, if you are uploading to youtube forget about AVCHD. You will have to convert everything to mpeg 4 in order to upload it, which will waste significant time and energy. Not something an employer will want to deal with.
In addition, the vast majority of your audience is not going to be viewing youtube videos on screens large enough for the difference in 480-720p to matter, much less 720-1080.
I would recommend a good DSLR with a macro lens myself, and learn how to use it. From what I understand of DSLR video, you lose a lot of auto functions, but if you are working in a controlled environment at consistent distances from your object, then it should work very well. Anybody with more camera knowledge care to take that one up?
EDIT: I was just looking back at your original post, does the class require an HD camcorder, or the ability to shoot in HD?
However, the key here is not actually going to be the camera, but you.
The problem with shooting jewelry, diamonds in particular, is that when looking at them with our eyes we have two separate angles. This allows for us to see significantly more fire (sparkles) in the diamonds than we can with a camcorder. Thus, you are going to want to select diamonds and other pieces that focus on brilliance, on the white light return of the diamond and jewelry. Then you will want extended footage in various angles, until you get glimpses of fantastic fire, splice those in as B roll footage in your overall films, and it will help the overall presentation, in my opinion.
You may want to head to a jewelery forum and talk to the ladies there. There is one in particular, I havent been active in a few years myself, called http://www.pricescope.com/forum/
if it is half of what it was when I was on it (i pissed some of the ladies off, unfortunately) they will be able to tell you exactly what you need.
In addition, you need to research how shadows can affect the image, and be very cautious of reflections. What you wear will show in the jewelry, so be cautious of that. You can also position yourself so that in your reflection the arrows and hearts of various cuts will show, which can be very important for overall impact.
I say keep it simple, I would say 480p, but it will probably make the store look better to view it in 720p, simply because people may think it sounds more classy to have it in HD. However, nobody is going to take the time to stream 1080 anyway...when you consider how quickly the average consumer moves on to other options when delayed. This is youtube we are talking about, make sure you focus on the jewelry.
(those tips above are just a few of many I can think of off the top of my head, to do this VERY well requires careful lighting, knowledge of the piece you are shooting, such as how it responds to different types of light and in different angles, and much more. Of course, you can just do it well without all of that, but, thats not my personal style).