@mynameistillian how about the sony alpha 6xxx series? the kit lens isn't very good for stills but it has OIS and is perfectly adequate for video. I have a 6300 and I'm very happy with it (mostly for stills and as a webcam though). I wouldn't go for the 6000 for video because it doesn't have a microphone jack and maximum 1080p50 (60 in ntsc maybe?) recording
you can even use an app connected via wifi as an external viewfinder