You're eligible for NHS care as a spouse (or fiance) of a British citizen, but you pay international tuition fees for schooling for a while until you have a more permanent status in the UK (I believe it's three years?). There's been plenty of debates about what country is better in what respects, I would just warn you to be careful making those comparisons, especially since you haven't visited yet. Both countries have their pros and cons ultimately, and you have to decide what's important for you.
I don't know if it's easier for her to get US citizenship; you'll still have to meet certain financial requirements to move her to the US, though this is mainly a board for people going from the US-UK; other forums might be able to answer those questions better.
I think it's best to focus on what you need for a visit, and then go from there; it can be overwhelming to be thinking about things way in the future when you haven't even been there yet. The grass always seems greener on the other side, and it's really hard to tell until you've set foot there and spent some time sorting stuff out.