Sorry to hear about your dog Sepen.
With respect to headphones, I'm not sure what type of budget you have (I know you said inexpensive, but that's of course relative), but I recommend the beats line. I picked up a pair of in-ear buds from them and I couldn't be more satisfied with the quality. I spent about $100 for my pair, but I believe they sell a slightly more affordable pair for around $60.
I've used Air Video (https://itunes.apple.com/us/app/air-...306550020?mt=8
) to stream videos from my server and it has worked flawlessly. I highly recommend it.
As far as apps go, here's a few that I can't do without:
You can't go wrong with Angry Birds, Fruit Ninja, and Plants vs. Zombies... as Mopetar said they're very popular and for good reason, loads of fun if you need to kill some time. Word With Friends is also a personal favorite of mine. If you enjoy Scrabble, you'll enjoy Words With Friends.
I also utilize my device for news, and depending on your interests you can find multiple news apps that will satisfy your hunger. I enjoy the Weather Channel App, Engadget, and NY Times.
Also consider downloading Google Earth, Facebook, Dropbox, Kindle, and Wikipanion.
Hope you have fun with your new iPad!