How did I miss this one? 
Anyways, regarding your question, if you ask me, I find a blog with a header, more appealing with a blog without one. You necessarily don't need something like a logo or something like that, but, yes, a header image is something you should opt for after due thought.
Loading times are ofcourse important, but how much delay do you think an image of around 500-600kb can cause? A header needs not be a very big image, but atleast should be enough to cover a the entire header part of your blog in terms of the screen width. This means that you should use a header with a width of atleast 1920px (given that most of today's Full HD monitors will be able to properly show the header) The code to automatically resize the header image, as per the screen width can be easily done via CSS, so, that shouldn't be much of a big issue. Image height depends upon you. Though, I like a header height of atleast 240 pixels.
If you want, you can take a look at my blog (MG) to get a feel of a blog with a header (though, this one is a what is called a responsive header slider based on a free plugin called Camera by Pixedelic. I have created a second one with just a header image and the blog's name for my second blog. Here's a screenshot of the header. This one again is responsive, and uses an SVG image file which is just 68kb for an image of such a resolution 1920x320 px (compared to an image file with extension .jpg or png, this is more than 10 times their size would have been). The text over the header is an overlaid text, that is not done on the header background image.
Image
The lines in this image are what are sometimes collectively called abstract art, and you can download one such files to be used freely without any restrictions whatsoever from any of the free vector image provider sites. Since these are vector graphics, you can edit these in appropriate application like Adobe Illustrator to enlarge the images as much as you want without any loss of quality.