Hi Glenn,
First off, that is a fabulous looking sign! I really like that detailed image with the pen and other items on the left. That is also going to be your most difficult area on the sign to "pop" Poplar blotches, so I do not stain / pigment / color it by hand or brush.
Do you have access to a spray device (HVLP, LVLP, Std Air?) I would spray a toning coat of dye on it to darken it just a bit, but you can't do that by hand and get an even coat in my experience.
As to the surface finish, a rattle can of Deft would work just fine, or you could use shellac as it's an interior only sign. Given the details I would stay away from Poly (in the event of dust or other nasties landing in the finish, Poly is more difficult than lacquer to smooth on an uneven surface).
This sounds more difficult than it really is, but that sign looks like a project to do "right' and one you'll enjoy for many years to come!
One last item I should have mentioned above, if you've some poplar scraps I would try a few different dyes / stains / coloration of choice to see which one you like the best - always easier to experience and fix a scrap (throw away) than to fix a project 🙂
Michael
