Testimonials aside, there is no doubt that white shows dirt/grime/whatever more than gray. Beyond that, it is just a personal preference of what you want it to look like. Gray grout is a much more traditional choice than white. If you are going for a vintage look, that would be my choice. On the flip side, if you are going to more a more "clean line" modern style, then I'd go with white.

We used Bostick quartzlock2 silver grey on some of tile. It kind of has a bit of a warm tinge to it. Its not as silver grey as I thought it would be but slightly a grey with a brown tinge to it. It might work well for you. The urethane grout should not stain like regular grout. I do know its a lot harder to work with though.

I have the Subway Ceramics Avalon / Minas with a medium gray grout. And a Shaw's white sink, if anyone is considering that, by the way. (My contractor could have ordered it directly, but at his request, I went through a tile store, and by the time everyone had put their sugar onto it, it was OBSCENELY expensive.) I'm not an installation expert, but at least with the Subway Ceramics, the installers use little plastic spacers between the tiles (I think some others have their own spacers?) when they put them up, they don't do it freehand, so how much grout you get is a function of 1) the limits set by the curvature of the tile and 2) what size spacers they use. So you might be willing to go a little darker with a smaller grout line, or with a handmade tile that refuses to go close together, you might want to stay light. The traditional color is close to concrete. But most modern people don't seem to like that, so do what pleases you!

We have gray grout with white tiles and I love it--our tiles were also DIY (and it looks like your dad's job was a bit better than ours was!) and the grout color hasn't been an issue at all. Sample boards are a great way to go, though--that's how we chose our grout. (A trick is that color-matched caulk is often cheaper than buying and mixing the grout, and you can get the same effect as far as the sample boards go.) Good luck--looks great!