I use a Canon S110 point and click digital camera. Honestly, for websites you don’t need much of a camera these days. The ones on phones have gotten so good, they’ll do just fine for any non-profesional level work. Obviously, more expensive models with the right lenses and features are going to give better results, but is it worth it? I’d actually invest in a tripod before a better camera. Having a high quality camera doesn’t mean squat if you can’t hold it steady. My lightbox actually came with a little one with an adapter for holding a phone, but mostly I just brace on a box because I’m lazy.
I think the two most important things for a light box is diffusion and volume of light. You don’t want focused spotlights casting shadows, and you want as much light as you can muster. You can get this with just some desk lamps and parchment paper, but for ~$50 you can get some nice setups online. I use one from LimoStudio, you can get it on Amazon. Comes with different colored backdrops and 2 LEDs. Made a HUGE difference in my photo quality. Folds up nicely for storage as well.