Hey Kirstine,
You can always make any post stick to the top of your posts page by making it a sticky post. Refer here: http://en.support.wordpress.com/posts/post-visibility/
You can do it by clicking on Visiblity on the Right hand side (where you click on Publish Post) and select the 'Stick this page to the top' option.
Regarding the picture upload. Its necessary to know whether you're talking about Custom Header or a Picture Upload in the Sticky Post. Only few themes support Custom header, so make sure your theme does support it. For uploading a width-size picture in the sticky post you can click on Insert: Image Link while editing the post and once you upload it to the Media Library, click on 'Insert into Post.'
Check support: http://en.support.wordpress.com/themes/custom-header-image/
You might also find this helpful: http://en.support.wordpress.com/images/
Cheers!