Current cameras

I believe most of us want a better camera than our phones for travel and/or kids.

Sony a5100 or a6000

These are the best cameras of 2014. They can be found as open-box on/in BestBuy for less than $400 with the PZ 16-50mm kit lens included. If you only want to spend $200 or less, then get the a5000 kit which is as good as the a5100 in real life except that low-light video has very noticeable noise.

The a5100 is better than a6000 on many aspects, except three important things: a) it does not have an EVF, not even an add-on option; b) it lacks of a quick menu which is a must if you go beyond P&S; c) it has half the fps, 6 vs. 11. The flip-up LCD and zoom rocker by the shutter are what I went for it for, plus double video bitrate 50 vs. 28 mbps.

Two lenses might be good to add: 35mm f1.8 OSS ($300~400) and 18-105mm f4 OSS ($500). Both are good for stills and video. 50mm f1.8 OSS is much cheaper but a little too long for indoor. These Sony cameras all have 2x lossless zoom integrated into the zoom rocker, very handy for video - the 35mm becomes 35~70mm (see details here).

Canon 70D

This is pretty much the only DSLR worth of considering for its perfect AF for video. The 18-135mm STM lens produces beautiful photos and video, but you might still want to add a Sigma 17-50mm F2.8 for low light for only $300.

Before and after you buy a 70D, be sure to check its focus. There are some, if not all, bad copies that cannot always do accurate focus if you use the center point AF while all other AF points always work perfectly. Check this thread for details. Although Canon has not admitted the issue, but based on my personal experience it is real.

Like above Sony cameras, 70D also has a 3x lossless zoom for video. However, there is a minor detail: once you enable this feature and start recording, no more any kind of focus adjustment, not even manual focus unless you have switched to manual focus mode before you start.

Two alternatives

Olympus E-PL7 or EP5: Finally there is an affordable M43 that allows IBIS (in-body image stabilization) for video! Now you can use all your favorite lenses, primary or zoom, with or without OIS, for steady movie.

Panasonic LX100: although you cannot change lenses but it comes with an excellent one, 12-37mm (24-75mm) f1.7-2.8. It even does 4K video!

Few shots from a5100 w/ PZ 16-50