Okay, I've been thinking about what exactly I would prefer, and after reading through the suggestions mentioned thus far, I agree that a selection box that's fixed in one direction and can be scrolled in the other direction would be an excellent way to keep the selection box as minimally invasive as possible. The reason I've worded it like that is because I simply can't decide whether to do it by x-axis or y-axis, so to speak. Those two options are actually inspired by what I'm familiar on other sites. BZPower uses only a single row of emotes that can be scrolled horizontally, while FiMFiction uses a square box about as wide as ten emotes that can be scrolled vertically. Perhaps it might be worth starting another poll to see which of those two orientations everyone might prefer.
As for my vote in this poll, I went with "by character", mostly because it's similar to what I'm familiar with on FiMFiction.