Hi.
Dpi shouldn't be that confusing at all.
Resolution=linking your document units to a physical distance value, base unit.
Inkscape works -or, rather- is hard-wired to 96 dpi. If you zoom in to 100% zoom level, you will see your work on screen exactly as exported at 96 dpi. That alone has nothing to do with the output options besides 96 being the default export resolution.
Note, it doesn't mean any other physical given distances would appear in their true scale by default on screen then even when at 100% zooming. Cause of this is your computer screen can display a fix amount of pixels on a fixed size, which can be anything. 96 dpi was chosen by the css workgroup (?) because it's close to the current regular screen resolution I guess.
Previous inkscape version was running at 90 dpi, while illustrator works at 72 dpi.
There is a slider in the preferences you can adjust your 100% zoom to display at your true screen resolution, so that objects would appear at their given physical sizes on screen.
Didn't had much luck with that myself though and it's only side related.
Dpi determines the dot/pixel density of your drawing. For printing text, 300 dpi is suggested, and 600 dpi for photographs.
(Latter needs a decent coated photopaper otherwise the ink would smudge and the print won't appear as sharp as the provided digital raster image.)
Note, that it's advised for printing readable books, which is read in a small distance.
Depending how far your banner will be looked at, you wouldn't need such a "large" resolution.
(Since the regular screen displays are hardly of the "retina display" quality, working at 100% is mostly impossible.)
The other thing to consider with the banner is, pdf printing. That way you can preserve all the vector content -no need of rasterizing *hopefully*- and your printer can print in the intended scale/physical unitse, i.e. 8ft. x 8 ft.
Filters are not supported by the pdf format, which makes them necessary to be rasterized for preserving their look.
Filters can be for example custom blending modes, blurs, drop shadows etc. Rasterizing them with the same as pdf dialog will render a raster double of those filtered objects at the given resolution.
BUT, raster images are heavy. Very heavy; double the size, four times more the number of pixels stored will be.
Currently a 10000px/10000px is quite laggy on my machine, larger raster images can melt your cpu away. Or the rip of the printer you print with. Even if you manage to save a large raster image the printer might give up on it.
All in all, you must keep the raster images size at a reasonable resolution.
6/6 ft=72/72 inch, which at 300 dpi would end up 21600/21600 px -would hardly work.
Same applies to embedded raster images. Adjust their size to the distance they'll be looked at.
Two times the distance of reading (2*15-25 inches?)->150 dpi is enough.
On the other hand if your embedded raster image is not large enough -in px size-, printing it in a too large size can reveal it's pixels.
Aside from these such a foam pattern may not work well from other aspects either.
Colour matching would need to be spot on -a cheaper printer may end up interpreting the neutral grey colour as a shade of green. Or yellow. Or anything in between cyan and magenta. Needs testing, needs proofing with the right material. Consult your printer.
It's not a good choice graphic design-wise either as it makes your text less legible.
Hope these make sense. Quite sleepy at the moment although could look up a dozen posts of the same problem.
To sum it up:
-consult your printer of the materials, printing method used, format requirements of the deliverables;
don't try to prepress, it should be their job. Colour can look different on your screen and on paper, ask for proof prints.
-Use pdf as your final print format.
-Make it simple, loose the unnecessary fancyness. Graphic design takes way more to learn than learning how to use a program.