One of the important factor when taking photos is lights. lots of it. Uou don't need expensive cameras to take a good picture of your pet.

The cheapest option to get good and soft lighting is to use the sunlight...hey it's free
When you use sunlight for your lighting, it's better to take the photo, in the morning, or in the afternoon, where the sun posisiton is low. This will give "better quality" lighting.
You can also get soft diffused lighting by taking the picture under a shade, or anywhere away from direct sunlight, but still bright enough for your camera to take the picture.

As for backgrounds, you can use anything or any colour, as long as it's doesn't have busy patterns as it will take the attention away from your pet.