I work at a book manufacturer, and we use .125" grindoff, with no ink in the grindoff area so you can design in facing pages spreads and not worry about an image that stops at the gutter needing to bleed into the grindoff.
We don't have any problems with crossovers. While they do require a little more care to ensure the image prints consistently, there's really no reason to avoid them altogether, assuming you are using a reputable vendor.
Totally agree about consulting the bindery first - always good advice to get it straight from the horse's mouth, since different shops have different requirements.
Also agree with setting up your document to the final trim size, making sure to extend bleeds at least .125" past the document edge. If supplying PDF, supply as single pages (not spreads - no need to re-work the document, just uncheck the Spreads button in the export PDF options). Crops marks (or any other printer's marks) are probably not necessary, but if you feel the need to add them, make sure they are offset by an amount that is greater than the bleed amount so that the crop marks don't print in the bleed area.