First, the bathroom floor...if you want hex tiles, the only reason you might not be able to use them is if you are planning on using a membrane like Ditra under the tile. Ditra, due to the nature of it's structure, limits tile to a minimum of 2". If you're going over cement board or another smooth-surface tile backer board on your floor, you can use small hex tiles. Simply ask him what his no kidding objections are to the hex tiles. There may be a real world reason why they are too small (like over Ditra) or he simply may not like working with mosaics. Find out why. For the shower floor, I usually stick to 4" or smaller, that way there are grout lines underfoot for traction. Plus smaller tile conform to the slopes of the pan without requiring cut lines at the intersections of the slopes in the pan. 2" squares are probably most common. Some people like the flat stone or pebble mosaic, but if you suffer from grout-phobia, the irregular spacing on those might scare you away. If there is a trend these days, it's toward large format tiles. They can lead you towards a contemporary design, but they can fit other styles as well. If I can steer you towards anything, look at "topical waterproofing membranes" for waterproofing your shower. Topical membranes put the waterproofing between the tile and the tile backer board, so the tile get adhered right to the membrane. It's a better way to control moisture within a shower. Two of the more common trowel or roll-on membranes are Hydroban and RedGard, for sheet membranes, Kerdi is probably the most common one. Probably the best, and easiest way to waterproof a shower these days is with a Laticrete flanged drain and Hydroban. You can wade through youtube videos or visit Laticrete's website to see what that is all about. Remember...unless you are planning on selling, I'll caution you to use tile sizes and patterns that you like, that meet the style of your house. Don't design for the latest fad, unless it's something that you really prefer. If you have trouble defining the tile size, pattern, or style that you do like, it can sometimes help to go to a site like houzz and look over bathroom photos there.

I'd probably go for a grey too. But first I'd try to find images of a similar color penny round with grey grout and make sure you like the look. I realized after looking at lots of pictures that I really like penny rounds but didn't want them on my shower walls because with grey grout they read more grey than white and I wanted white tile walls. I don't honestly know that much about the different brands of grout. I know there have been recent-ish advances in grout that makes epoxy or something very like epoxy grout easier to work with. The tile people in the bathroom forum probably have explained this if you do searches. I'd probably just defer to my tiler if I trusted him or her. (Just an FYI, according to my GC it wasn't possible to match the regular grout we used for wall tile to the epoxy grout we used for the floor so I had to pick two different greys.)

I totally understand your concerns about maintaining congruity with the era of the house. My personal feeling is the the mix of old and new is what makes design interesting. I'm not a fan of walking into say an all modern room in a vintage home. It's jarring. But intentionally integrating a modern element into a more traditional space can be the spark that "makes" it. So, for your bathroom, the larger hex can be a "riff" on the classic tile - that updates it while playing homage to the house's era. At the same time, the use of a solid blue on the floor is already a more modern use of the material. So you could go with a smaller blue hex rather than the larger. I would choose your grout very carefully. I personally don't like a ton of contrast between the tile color and the grout. It just looks really busy to my eye. I also am imminently practical and would never put white grout on a floor. Something in the medium gray range would probably work best but I would have your tile installer make you up a couple sample boards once you get to that point. Smaller hex in a solid color: Grout similar to tile color:

I used Whisper Gray Tile Shop grout and it's perfect. It is the lightest gray available. I grouted a demo sheet myself first to check it out. Great $20 spent to try a grout color before you commit!! You aren't supposed to use Sanded Grout for Polished stones as it could scratch them. We ended up doing it anyway (not heeding my own advice I guess) but our Tile Guy was very careful with a sponge and delicate. Sanded grout holds better than Unsanded also. On our honed floor we also did sanded. So for my master if I have this dilemma, I would go Epoxy grout. More $ but best choice. My bathroom I'll share pictures of will hardly be used (off a bonus room, not any bedroom).