Let’s define “gutter” because it can mean different things to different people. I’m assuming you’re referring to the place between the pages where they meet and are bound, right? In a saddle-stitched magazine (staple binding), where it can open up and lie flat, a full spread across the gutter is common. With stitched signatures or perfect binding, this is problematic since the book can’t be completely opened up flat. This creates, as you know, an awkward space that isn’t fully visible. If you have an unusually composed photo with a big dead space in the middle, I supposed a full spread could actually work. Otherwise, it’ll be difficult to pull off successfully.
I’m assuming full horizontal bleeds as well since you’re concerned about the gutter. There’s less of a problem regarding the gutter on full-page bleeds, and I wouldn’t avoid them at all. You still need to account for the dead gutter space, however, and crop your photos accordingly. Speaking of gutters and perfect binding, there can be problems regarding the printing extending all the way to where the pages are glued (the ink can interfere with the glue), so this is something to discuss with the printer/bindery. They might want a 3mm, or so, of blank space there (that will never be seen when the book is opened).
Black? Why would you make it black? Why would you want a black stripe in the gutter? This makes me want to repeat again that you really ought to follow my and @StudioMonkey StudioMonkey’s advice about designing a few pages, then having a good designer look at it. The unused or only partly usable space taken up by the gutter really does need to be thought through carefully. You might want to find a similar book, see how they’ve treated it and how much blank space they’ve allowed for it.
You can do it either way or both as long as it’s part of the design, well-planned and done consistently. Again, though, if this is perfect bound, you’ll need to leave a tiny bit of printer-specified blank space for the glue. If it’s hardbound and has a sewn signature binding, this wouldn’t be an issue other than the fact that whatever imagery is deeply buried within the depths of the gutter will never be seen.
I don’t know how much control you have over the printing and binding, however. You’re self-publishing, which could mean anything from you just submitting what you’ve done according to written specs to a mass producer of self-published books to a more traditional printing and bindery company that will work with you and provide suggestions.
You mentioned celebrating 40 years of photos, so you want this done right. I’ve seen more than one book laid out in a way that doesn’t adequately take into consideration the binding and the gutter, which you apparently already realize.
There are lots of other production issues too. Old photos will be scans from film, right? How were they scanned? What’s their resolution? Any black and whites? If so, will you be running them 4-color process or using duotones or tritones? What paper stock are you using. What weight? What about the cover and the spine? What about media coatings, like spot varnish or an aqueous flood finish. Do you understand all these things and how to work with them. Are they options with the printer/publisher you’re working with. What layout program are you using for this. I hope it’s not something like Word.