Here, the Surface 2 is perfect for work, as you get free Office and have word, excel, power point and outlook. E-mail you don't need to worry since Microsoft got the Mail app to be a great app.
However, you need to use IE for your browser, you can't use other browsers. Yet IE itself is fluid and fast, contrary to popular belief. Video Watching is also having no problems (a lot of alternative video app if the native one doesn't suit you, and Xbox video lets you buy movies). Unless you have movies with really confusing formats, you won't have a problem.
The Surface 2 is small, fast and tenacious. Especially with the keyboard attachment, you can type comfortably (Type Cover 2) and get work done fast. With touch integration of Office (combining touch screen with typing), you get work done. Fast. The battery life also holds up to 12 hours for me with light use, though Microsoft said 10 hours of video playback. NOTE however that the battery life will at first be only 6-8 hours only. But with repeated use, the battery life WILL improve to reaching 12 hours.
Note taking is easy with OneNote app that Microsoft has beautifully built. You can integrate photos into your OneNote notes using the front or back camera of the Surface 2.
Microsoft's services are also top notch here, with Bing (News, Health & Fitness, etc.) and Calendar, so you could keep being updated with news of your surroundings.
The drawback though I think is not being able to install .exe apps or any program for that matter, no touch-pen recognition and lack-of-games (you could argue this). If you are looking for famous popular games such as Plants vs Zombies or Candy Crush, you won't find it here. But there are a lot of great games provided by Microsoft (look for an Xbox banner on the app picture) or other great games such as Halo: Spartan Assault and Asphalt 8: Airborne. If you're a light gamer I think games wouldn't be a problem (as I myself am a light gamer now, and occasionally play Microsoft Solitaire or Mahjong, with a little bit of Asphalt).
Bottomline, the Surface 2 will fill your work requirements greatly, has a long battery life, relatively small in size, able to play media and entertainment, and a great way to be productive in general (either through note taking, finishing up essays, and those other stuff). The drawback of not being able to install apps is also a plus for me, as I don't get tempted to procrastinate as I can't play my favourite heavy games (League of Legends, Fallout, Crysis, Dawn of War, Skyrim, etc.)
**P.S. Twitter and Facebook apps are working great, and so is Skype. You also could multitask (split the screen into 2) such as watching a video and typing at the same time. I personally recommend you to get one, with the Type Cover 2, as it will fit your needs really well.
***P.S.S. If you do get one, I'll tell you the essential apps you need to download that would make your life way easier.