-OK, so the options are (assuming a standard 32pp picture book):
Yer basic epub, which we will call 'vanilla epub'. This can be read by just about anything and will convert easily to mobi format, for Kindle; your book can be made available on every platform.
The downside of vanilla is that you can't do any layout or typography. Text and pictures will exist essentially in a stack - a block of text, a pic, a block of text. You won't be able to have text going over the top of images, or appearing to one side.
(You could theoretically have picture book pages with integrated text which are rendered as flat images. I would avoid this, because vanilla epub is for such a range of devices - from little phone screens to b/w e-ink screens all the way up to tablet and PC displays - that you are inevitably going to end up with quite a lot of display sizes that make the text unreadably small.)
You can't do much in the way of playing with fonts or text layout. Also, because the typeface and its size is under user control for the most part, you don't know how the pages will fall - at certain type sizes things will reflow and sever pictures from text.
Basically I don't recommend vanilla epub for picture books unless you are doing something very simple, like, say, Beatrix Potter. You get a wider audience because you include e-ink readers, but the book looks rubbish on e-ink, so it doesn't feel like it's worth it. (It's very annoying to have to write disclaimers into the product description, too - "WARNING: This will look crap on Kindle.")
So I think the thing to do is to target tablets - iPads and Kindle Fires. These can support fixed-format picture books, using beefed-up EPUB in iBooks and in KF8 format for Kindle. These picture books essentially work like PDFs - exact copies of the print layout - and can have text overlaying pictures, and basically all the good stuff. Text can be zoomed or read aloud in some platforms. The bad news is, producing a fixed-format picture book file is not that simple. It requires HTML coding skills, essentially. This is how I produce picture ebooks - in the sense that I tell a much cleverer man in another office what I'd like done and he does all the coding.
If you have access to a Mac, then you can do this quite quickly and easily in iBooks Author (which is free); and it makes publishing to iBooks quite simple. Again, the bad news is you need access to a Mac running the latest system software. Perhaps you could borrow a MacBook for an evening or two?
The downsides of iBA: you only get to publish into iBooks. That isn't too bad, in my opinion - Kindle still isn't very focused on this kind of content. Also, iBooks Author is really intended for textbooks and the like, so all the basic templates are divided into chapters and sections etc. Perhaps there are custom templates out there now which remove those divisions?
If you can't get hold of a Mac for a bit and you can't code HTML and CSS etc, you could look into paying someone to do a fixed format EPUB/KF8 file. I am not sure how much it'd cost (when I outsource these, we get a bulk rate.) The problem here is that picture ebooks don't make very much money, at all. So you might not have a reasonable expectation of getting your money back if it costs more than a hundred quid or so.
