In our 360 product photography projects we usually produce 20-36 images per product and this is what we recommend to most of our clients. 20 images in particular offer a good balance between smoothness of the animation, download/wait times, and the amount of required photography and post-production efforts.
The next question to consider is viewer dimensions when placed on your web pages and its zoom depth. For example, if your viewer is configured to be 500 x 375px on the product pages and you want to support x 2 zoom, the images should be at least twice the size of the viewer to present in good quality when zoomed in, or about 1000 x 750px (NOTE: for sharpest product presentation we recommend producing 360 images that are just a bit larger than what they would appear when zoomed in full). This will result in JPG images being ~80-100 KB per image for an average product image with no background and with a decent JPG quality, which is a ~2 MB download for 20 images. For the average broadband cable speeds at about 3 Mbit/sec (read more), this is ~4-5 sec wait time for a complete view to load. This wait should work well for the majority of e-commerce applications. Note that WebRotate 360 viewer downloads and shows the first pre-loader image immediately so your web page visitor has something to look at while the rest of the images are downloaded and processed.
Same applies to the full-screen mode where to keep the original sharpness of the images you will need to produce images that are noticeably larger than your original viewing box on the product pages. WebRotate's 360 product viewer has two settings that control image presentation in full screen mode (maxZoomFullScreen and fullScreenStretch).
When saving images, always use the Save for Web option if available so you can optimize your 360 degree product photography specifically for Web presentation. Don't over-optimize as even high quality JPG compression (~80%) will result in relatively small files that should work for most 360 product presentations.
IMPORTANT: Due to the zooming algorithm used by the Flash player/browser, it's important to keep image width to height ratio same or similar to the ratio of the viewer. This will ensure that you have sharpest presentation of the images inside the viewer. For example, if your viewer is 480 x 320px, the images can have either the same size or smaller (recommended for best quality if no zoom/full-screen is required) or stretched proportionally, i.e. 576 x 384, 720 x 480, 960 x 640, etc.
You can download the FREE edition of our 360 Product Viewer here