Background Images for your theme can be any size you want, but it's important to note that they don't stretch when a fan resizes the window. We also don't resize the image after you upload it. So make sure you upload an image that's at least the width of your theme. Most themes are around 900px wide.
Another important thing to remember is that the Background Color set in your theme options, will always be behind your image. If the image is 1000 px wide, whatever size your fan enlarges their browser window passed 1000 px, that background color will show. It's a good idea to pick a color that blends with the image.
If you're using a pattern background image, which is actually what we suggest you do (if you use an image at all), you should tile it. There's a checkbox below where you upload, that will give you that option. Tiling the image makes the image repeat over and over again, so no matter how big your fan enlarges the browser window, they will always see your pattern background image. This is why a pattern is so much better than a photo of your 12 year old birthday party at Adventure Land.
If you do decide you can't live without showing the world what riding the Alfie Swings is like, then we suggest you use the Center Background Image option. This will make sure your teary eyes and dangling feet stay centered when a fan has their browser maximized on a 27" iMac.
Beyond these tips, we don't have much more to offer. Art is hard, so be patient and try not to do too much!