Spherical panoramas have a 2:1 aspect ratio because the field-of-view is 360° x 180°. You obviously need enough photos to cover the whole surrounding. If you use stitching software, then you need to have some overlap between images and will take slightly more images than enough to cover exactly the 360°.
As a minimal setup, a single camera with a lens on each side, mounted on a tripod, can do this. If you use such camera, a remote-trigger device, like a cell-phone is needed to trigger it.
Otherwise, most camera will do. If the camera has manual controls, including manual focus, then it will be easier because you can ensure consistency between shots. With a smaller the field-of-view, more shots will be necessary. Considering your resolution requirements are low though, I would opt for something very wide. With a fisheye lens covering 185°, you only need two shots. A compatible camera is obviously required.
Ideally you take the shots while rotating around the nodal-point of the lens. Doing so precisely by hand is nearly impossible, so most people use a panoramic head. If your lens is fixed focal-length, there are some models which are made precisely for a combination of camera and lens and need no adjustments. Otherwise, you need to calibrate the head to your particular combination of camera and lens at the focal-length you intend to use. This is not hard, just tedious and you have to be careful not to accidentally change things. The closer things are to your camera, the more important this is. For an indoor spherical panorama, consider a panoramic head essential.
Most stitching software can stitch such images and the success-rate depends mostly on the subject matter. You can even try free software first and if those do not work, move on to a paid solution. A good number of software now attempt to automatically stitch images which works surprisingly well. One such is MS ICE which I reviewed here. It's hit or miss. When it works, it does and when it does not, well, you have to trying another.