Neuroscience was my back-up choice after Medicine, I also think it's a fascinating topic.
Books seem a little in-depth though, or maybe that's just me.
What I did during my A Level year is watch science documentaries about topics that interested me. There's an interesting documentary I remember watching about heart transplants, and using stem cells to help patients with cardiac problems in the future (I'll try to find the title for you). I've found the Horizon documentaries to be good as well.
Another thing you can do is follow the news revolving around neuroscience, or medical research in general. There's the typical sciencey magazines out there, but the internet is also very useful. I use tumblr a lot, and follow a lot of neuroscience blogs, which are updated with the latest research:
http://neurosciencestuff.tumblr.com/http://neuromorphogenesis.tumblr.com/I guess I prefer the simple stuff.
There's also a good TED talk about mirror neurons:
http://www.ted.com/talks/vs_ramachandran_the_neurons_that_shaped_civilization.htmlOh, and this website is helpful for finding documentaries:
http://topdocumentaryfilms.com/The Health section of the BBC news website is also pretty useful at times. Particularly when looking at what is happening in the NHS in different parts of the UK. StudentBMJ also seems to be a popular one.
It's great to hear so much enthusiasm. Apologies if you were mainly looking for books though. I'm a very internet/geeky person.