Almost any camera will do including a cellphone for what you are doing. Most important will be for you to buy a few video lights and stands with soft boxes. The reason is that if you are showcasing something, you want as much detail as possible and in order to do this you need to shoot at an ISO in which the camera will have the best performance. This is always the native ISO, which is between 100 - 400 for most cameras. Without boring you with unneeded technical explanations, you want to shoot in very bright conditions in order to have the best looking video. Using your own lighting will make everything bright and reduce shadows. Soft boxes reduce the harshness of light and will prevent hot spots or clipped highlights.
The camera recommended by popatim is a good one. You can also consider the Panasonic G5 with kit lens which will run about $370. I would recommend however the Panasonic G5 with the Panasonic 20/1.7. This combo should run about $500 however the lens if very sharp and is great for capturing details. You would want to shoot at F2.8 (or F4.0) to get the best in sharpness and at this aperture, you will have a good amount of light gathering from the lens (much better than a kit lens). This will give you more options with lighting.
Overall, in importance you are looking at the following order:
1. Lighting - without good lighting your video will look like crap (maybe $300+ for a good setup)
2. Camera - this is not too important, as most modern cameras are very good in video
3. Lens - most lenses are very sharp however this still makes a difference
4. Tripod - important to have, but almost any tripod will do. You can pull it off with a stack of books too
Keep these things in mind when you are setting your budget. If you have a small budget, spend it on the lighting and use your cellphone (provided it does 1080p video). It will be adequate until you start making some money. I would then go for the $500 option in the G5 (or similar) and Panasonic 20/1.7.