To make the image look great on my background and avatar

what is the perfect size to use

Don't know what you're asking. Your avatar that is visible right now is fine. You can also have a signature that is displayed below your posts. When someone clicks on your name they can view your profile where a background is displayed. You can also have a user image. What exactly is your question, because technically your avatar will never 'be on' your background. Are you just asking how big your background image should be? ..or did you mean to ask what size signature?

how big my background image should be to look the best?

It depends. A good minimum width would be 1024 px wide, but the left and right columns are about 200 px wide, so they'd cover up some of what you're trying to display. You can also set your background to left-align, center, or repeating (works best with a pattern). If you wanted one large image, then 1920 px wide would cover most large monitors. For height, 1020 px works.

This post was edited by ericswanson_19 on Dec 17 2013 11:22am

Profile background size is dependent on your monitor size, it will look different for other people if they have larger or smaller resolutions
You should also be aware that there are rules for avatars/signatures/backgrounds
You can find them here: http://forums.d2jsp.org/topic.php?t=62261140&f=111

Right now your avatar is too large, but it can easily be fixed, just ask around the request section :]