I have had both. I think an infrared lamp is a good choice and may be more energy efficient because it's "instant on" and you will only have it on when you need it. A heated floor is nice, but it's not an "instant on" item like the lamp. Also, the floor takes a little while to heat up unless you have it turned on in advance or all the time...and you won't feel as warm as you will with the infrared on you. Just bear in mind that the infrared will be warm only when standing directly beneath it, but you will feel cool as soon as you step aside from the area it projects down to. If you have a big bathroom and will be moving to different areas, you may want more than one.

I have PB in one of my bedrooms. It's a wonderful color. I would look for a white that blends with your tile. I think PB will be fine with that. Antique white, though sounds more yellowy or beige and I don't think that would look as good.

I'm a huge CC fan, that's no secret, but if you can't get that I found a nice crisp 'classic' white is Behr's "Clear Moon". It's got 'body' to it, not too yellow, gray, pink, etc. Just a 'clean' white. (Color obsessive that I am, I pored over many manufacturer's whites before I found one I wanted for my ceilings and other areas I did not use Cabinet Coat. A 'neutral' white that would work with about any color on the walls, cool or warm.)

I have to comment on the 4" granite battle. I didn't want it (obviously). GC brought it up and DH wanted it. I finally won the battle (took at least 1+ week of convincing and some cost difference before DH agreed). Granite fabricator (owner of shop) came in today to measure for granite bath vanities. He admired the backsplash and said "see I told you it would look better without the granite backsplash" to the GC. Ha! I can't figure out why GC was pushing that so hard--it wasn't going to make him any extra money. I think he and DH were just stuck with the picture that "everyone" does a 4" granite backsplash. Anyway--on to the backsplash material. It is honed travertine. I got it at the tile shop in town. Even got it on sale! I'll post the link of the actual tile. I sealed it and it is working out well. I sprayed water on it to test it and the water just beaded up beautifully on the surface. Here is a link that might be useful: Claros Silver honed corinth