What background or how can I improve design of my website?
I would go with a cool grey to let your content be the focus. If you're looking for a pattern you can find one and recolor it, or create you own. But most modern websites have very simple backgrounds with subtle patterns or textures.
Usually I find it hard to guess which color will work well. A better way would be to play around with the colors and see which color turns out how in the whole context of the page. You can do this interactively on your own webpage by using Colorizr.js.
Maybe you could post later which colors you finally chose.