There is no limit to the size of the picture. Keep in mind if you make a large image, then this is what people will see. If you make your image very tiny, then people might not see it.
Knowing how to design a layout, for a web page, or website is very important. If you make your picture very large, then your picture should grab everyone's attention, and people might not see if you have something else on your web page, or website do to your large image.
Think about which devices you want to use. You can make your pictures big, or small on your layout, and if you want, you can use all devices. If you decide to use mobile technology, then you have to make sure you understand what you are doing, or else you might have problems with your layout.
Whatever size you want it to be, there is not specific size. Responsive websites automatically resize the image based on the info in a CSS file. You do not want them so small that they will display properly on a device with a small screen like an Android: (portrait: 240×320) and on a desktop, still be that size. Use CSS to control how your page displays it s and you should have no problems.
Here are the most common device resolutions: http://screensiz.es
If you're using a single image (as opposed to multiple ones and @media queries), 1920 x 1200 should cover it.
As large as you want.
This should help you.