Mobi and epub can both contain images if they're set up right. I would do giveaways with both formats. HTML can be offered as a zip file with the images in a separate folder.
I might even do PDF giveaways, although those aren't good for ebook reading devices. PDFs sized like paperbacks aren't too bad on them, but letter-sized PDFs are almost unreadable on tiny screens, and the way PDFs work make them bad for portable devices.
A lot of portable readers are black-and-white only, so you should take a look at your images in black and white and see if they're still clear enough. (If they're not, there's usually a way to get them touched-up so they don't look bad, even if the color details are lost.)
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