Hi Liz,
Welcome to Digicamhelp. While we don't recommend specific cameras at Digicamhelp, we can help with features you should consider for your photo-taking needs.
In my 35 mm days, I took most portrait photos at a focal length of about 85 mm. Saying that, this length may be a bit too short for your needs since you are standing away and beneath the podium to take shots.
Some of the fastest digital cameras on the market are digital
Single
Lens
Reflex cameras. They have high quality lenses and take interchangeable lenses. They are, however, at the high end of the price range and lenses are usually sold separately.
If you're not looking for an dSLR, you may want to consider a prosumer digital camera such as the Nikon 8800 (8 megapixels), the Olympus 8080 (8 megapixels; no image stabilization) or the Panasonic FZ20 (5 megapixels). Since you mention being unable at times to hold the camera steady, consider a digicam with image stabilization. All three cameras I mentioned have fairly long telephoto lenses which can be used to zoom in to take a portrait shot.
I happen to own a Panasonic FZ3, the low-end of the FZ line. Compared to the other digital cameras I own, it is very fast and responsive. The image stabilization works well, in fact, I find it quite amazing and would personally never buy another digital camera without it. It does not have an hot shoe, which you probably need for an external flash.
One of the best places I know to help you learn about the features and speed of a digital camera is at dpreview. They do extensive testing and offer many in-depth reveiws.
http://www.dpreview.com/reviews/They also offer side-by-side feature comparisons:
http://www.dpreview.com/reviews/sidebyside.aspI recommend you boil your choices down to about three cameras, then go to a local camera shop and hold each in your hands. As you imply, the ergonomics and how a digicam feels in your hand is very important.
Besides focal length, speed at which photos are written to a memory card, hot shoe and, possibly, image stabilization, if you buy a prosumer camera, also consider one with an articulating LCD screen (ie. it can be moved in different positions so the screen is easier to view if you need to hold the camera at various angles such as over your head or at waist level).
Many advanced digital cameras let you view an image immediately after you take it. It flashes on the LCD for 1, 2 or more seconds so you get an idea if it is in focus. You can also preview each image in Record mode and then press a lever or two to zoom in close, and move to various areas of the image for review.
To be honest, most digital cameras have quite a few buttons. It's difficult to avoid them if you want to find a camera which offers some creative control, such as depth of field (shallow depth of field is often desired when taking portrait shots).
I hope in some way these suggestions and comments help. If not, or it your have further questions, please ask away.