If you want to keep the background to 4:3, you WILL end up with black bars as 16:9 is wider than 4:3, and if you fit height you will end up with black bars on either side. The solution is to pick a height for your background, eg. 768, then work out the largest width for all the aspect ratios you want to support. Eg. for 16:9 the required width will be 768 * 16 / 9 = 1366 rounded up. With a 1366x768 background, you're probably not going to get bars on most popular aspect ratios, but you will need to work this out for yourself.