My most used app is GoodReader for viewing PDFs and giving talks. I also use my iPad for reading papers from journals and reviewing papers for journals. I keep manuals for my car, my electronics gear, blood work scans, etc. in there. It is great for that. Plus, it links into Dropbox so I can get to that material from any place.
Then, I use magic piano probably every day too....more for stress relief. I use the YouTube app a lot to follow tech vlogs and reviews. I have a lot of apps, too, from games (I'm not much of a gamer but I keep several around), to recipe apps, to kindle books, to magazines (computer stuff), comics, and movies. I only really watch movies on an iPad when I travel, though. I probably have 300 apps on iPad. I have a 3rd gen and a mini, as well as two other android tablets. I have several pcs and laptops, so I use the best tool for the job and hand. Sometimes I will take my iPad and keyboard out some place to get some words down when equations aren't needed.
Yes, it sounds like you have some other motivations beyond just work. As I mentioned more than once, you can do what you want on an iPad. The apps are there. Things won't be as optimal in the work department, but maybe an iPad will serve your overall needs better. It is a very powerful general purpose device, once you learn all the various details to get what you need from it. It is certainly a lot more fun than any windows machine I have ever owned.