When in doubt, save your image in both formats and choose the one that gives a smaller file size. It's hard to make a background image that won't render your text illegible for a lot of people. Backgrounds look different on different combinations of hardware and software. With such variation, finding text colors that stand out enough from the background is next to impossible. But you can't go wrong with plain white.
Some people have to access the Web without graphics.
Visually impaired readers can set the text size larger to make it easier to read. Blind people can use browsers that read the words to them or transliterate them into braille. Search engines can index the words. But pictures are meaningless to a reading machine or an indexing program. Some people have access only to Lynx or other text-only browsers, and others prefer to use a graphical browser with images turned off for speed and economy.