Going back to the original question: I'd avoid BMP altogether (it's a terribly old-fashioned format); I don't think that Poser can read PSD files, but if it can there's no advantage to using that (proprietary) format in preference to TIFF; I'd say PNG and (lightly compressed) JPEG are the best options. For single channel maps (e.g. bump, displacement), consider saving these as grayscale images to conserve disk space.

With an eye to the future, we could see JPEG-XR, PGF or BPG start to replace JPEG and PNG in the next year or two.

Vector artwork is an entirely different kettle of fish to pixel-based images, more akin to a 3D mesh than a photo. Some 3D apps will let you import Illustrator files and extrude / lathe them into 3D shapes.

As far as I can tell, no 3D program (and certainly not Poser) has color management built in (I believe there are plug-ins for C4D and LightWave). They expect incoming images to be in sRGB. No matter what color space you use or how the image file is tagged, Poser will assume that it's sRGB. If your workflow involves any other RGB space (e.g. Adobe RGB), you must save all your assets out in sRGB or you will get all sorts of problems with inaccurate colour.

The TIFF file format - and other less well-known ones such as JPEG2000 and MrSID - support multiple levels of resolution which would have obvious benefits for 3D mapping. The way it works in TIFF - a pyramid structure - creates enormous files. JPEG2000 and MrSID use more elegant and compact wavelet based structures capable of significant compression with both lossless and lossy options.

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