I second Tekkonkinkreet [trailer]. Doesn't always make a hell of a lot of sense, but oh so enjoyable to watch.
Wings of Honneamise [trailer] has gotten a lot of good mentions around these boards lately and I find that gratifying since it's been among my most favorites for two decades now.
Macross: Do You Remember Love? [movie] is another classic that distills the 36 episode series into about two hours. Obviously, a lot is left out but all the high points are there and it's another that's just a lot of fun. The final battle song is an anime mainstay at this point.
Finally, Sword of the Stranger [trailer]. This one is great for good old fashioned sword action. The story and animation are noteworthy even by modern standards, so it's definitely worth a look-see.
I used WDTV Live HD for many years. It can run just about any codec if you're looking to stream your own content (or "acquired" media). It also has Netflix and few of the other popular streaming networks.
If you want to focus on streaming Netflix, Hulu, Spotify, Amazon, etc... you should look at the Roku 3 or the Amazon Fire TV.
Nodame Cantabile because you liked Sakamichi no Apollon. There are 3 Nodame seasons. The show is about classical musicians.
Honey and Clover is more about life. I'm not sure I call it a slice of life series, but the structure is similar. Anyway, if you like relatable, this is a good choice.
I second the earlier recommendations of Arakawa Under the Bridge and Maison Ikkaku, too. The latter is a bit long though and it can get frustrating with the one-step forward, two-steps back progression. The ending however was so very satisfying.
Drew is great, no argument, but Dan was the one who motivated me to sign up after all these years. He's mesmerizing like some sort of 80's-retro Svengali. The pair are perfect together, but if you feel you must award Drew with the MVP, then Dan deserves an assist for his contributions. Metal Gear Scanlon is fine but they need to post another Demo Derby.
This was my first thought as well. I used to like Kotaku back when 1UP was still around, but over the years they devolved into something unpleasant. I am sure Patrick knows this, so perhaps he can help right that wayward vessel. Polygon has always been unreadable for me. A grand experiment in ego.