I’ve been a vocal supporter of Canon in the past, both for their dSLRs and their P&S cameras, but rest assured, these days are over. Canon is left behind in dSLRs when it comes to video, while they consciously removed existing video features from their new P&S (exposure lock and custom colors are now omitted from most new P&S), making them utterly useless. I sincerely can not recommend any new cheap Canon P&S anymore for video, while their 3 year old models performed better in terms of feature-set.
Sony has made some evolutionary steps in the right direction, but it’s Panasonic who has come to its own with their 4/3s cameras (particularly the GH4), and their P&S line. Their latest offering, of their popular LX line, is the LX100, arguably the best P&S ever. It comes with a large 4/3s sensor, a very fast f1.7 lens (with a 43mm thread to add filters!), 24p/30p/60p frame rate, 100 mbps bitrate at 4k resolution (!), full manual control, and some color control too.
Basically, it makes it the perfect video camera for indie filmmakers who don’t want to bother with lenses (e.g. if they shoot guerrilla-style all over the place), while retaining the large sensors found in dSLR-type cameras. The 4k quality you’re going to get for $900 is unparalleled too.
Now, if you don’t want to bother with 4k editing (which can be slow), then the tiny Canon EOS-M mirrorless camera is still the best bet (coming with all the video features one would expect from a Canon dSLR). It’s now selling for about $230 on eBay, as new, which makes it very cheap for what is capable of. You’d still need to buy 2-3 lenses for it though. Overall, with a wide prime, and a cheap zoom you’re probably be paying about $500. Which is still cheaper than the LX100’s $900. But you don’t get 4k or the ease of mind of using a P&S.
Personally, for the type of videos I shoot (art-type stuff), these are my best options right now.