Look for the ones with AMD chips, especially the E350s and E450s, as those come with HDMI out and most will hold 8Gb of RAM and do 1080P. A good place to start would be the Asus EEE "B" series, with B standing for Brazos. I have one and its fricking great, 4 years on and it still types well, gets nearly 4 hours on the battery and with 8Gb of RAM everything plays nice and smooth.
But if you want a really cheap media tank instead of using an old lappy look at th E350 barebone kits as I've seen them on sale at Amazon for around $100 with case, I've built quite a few of those as both media tanks and office boxes and they are really sweet, use less than 20w under load and will play just about any format. A word of advice though, if you get one make sure your player is set to use DXVA and get the codecs from either AMD or the excellent CCCP codec pack as the E series APUs are really designed for hardware video acceleration and not having that turned on ties a boat anchor to them system. Using a player without DXVA a 720p video was hitting 80% CPU while the same video with DXVA was using less than 15% so it makes a HUGE difference when it comes to performance.
As for TFA how anybody would trust some large megacorp after the Snowden revelations is frankly beyond me...I mean do you have ANY idea how easy it is to know pretty much everything about you simply by having your browsing history? Everything from what kind of porn you like to what medical issues you have and what beliefs you hold can be gleamed from that sooo easy its just not funny. This is why I have one company for mail, another for search, and made a throwaway account just for my android phone, giving ANY company THAT much info is just creepy.