Entry level DSLR + lens(es) for ~$1000

Hi there,

I've been casually film-making for a couple of years, but I'm about to start properly studying film and kind of stepping my game up (in terms of seriousness of productions, etc). Anyway, I've used friends DSLR's before (mostly the Canon 550D), without any real knowledge of the technical side of them - but I liked the result. So I kind of figure I should properly get my own equipment, as it's kind of annoying for both of us for me to constantly be borrowing stuff.

Being a student, I don't have a hell of a lot to spend, and am looking at trying to spend around $1000NZD ($850 usd - pushing upward if justifiable). I'd like one solid lens (I did find using stock photography lenses sufficient, but I'd like a more suitable lens) to start off with, obviously getting more in due time. I also have a rather rubbish tripod which I'd like to replace, but before that I need to get a somewhere near decent mic + steadicam. I was initially looking at the Canon 650D, but recently, my readings and youtube viewings have lead me to really want the Nikon d5200. However, this is top of my budget, and using stock lenses - not giving me much to play with in terms of other equipment.

Any thoughts, advice, etc, given my budget?

Thanks in advance
The advantages of the Panasonic range, in my opinon are (only referencing the gh3 here)
1) It's a good stills camera, which you may like if you're an amatuer photographer, or like time lapse work.
2) 1080 60fps (fairly specific feature, that realistically may not be used often)
3) This is purely personal - but I prefer the shape of the panasonics. Granted I haven't picked up a blackmagic (considering they haven't been released!) - but the shape looks a little awkward
4) It has a viewfinder (which, a lot of people don't think is needed, but I find very useful in setting up shots). You can of course add one to the blackmagic, but it takes away from the "pocket" aspect
5) In camera len distortion correction
6) Weather sealed. I mean, i wouldn't take it in the rain, but it gives you a little less to worry about in borderline conditions. As fas as I know, the blackmagic is not
7) Autofocus (I'll throw this in, even though I never use it, and most people don't - but a few may find it useful for whatever reason)

Of course, the Blackmagic has it's own advantes
1) Size (although this is debatable - by the time you bring your lenses and extra kit, I'm not sure how much difference the smaller body really makes)
2) Better dynamic range (quite significant)
3) Price
4) Larger/better lcd
5) RAW codecs
6) The codecs it uses gives it truer colours and few artefacts

At the end of the day, both cameras going to give you great images, so it really depends on what you value more.

Not that anyone really asked, but there you go.

(I referenced this a bit, btw http://herefortheweather.wordpress.com/2013/05/03/bmpcc-what-about-the-pocket-cinema-camera/)