https://www.youtube.com/watch?v=r6bzQfZ8OCQ&feature=related
Disclaimer: I am not an experienced filmmaker.
Personally, the GH2 or GH3 is on my wishlist.
If you're buying used, then there are probably a bunch of specimens, both GH2s and 60Ds, on Ebay and any number of camera stores' used departments, Craigslist, etc. If you're buying new, I think that Adorama and Amazon are not even selling new GH2s (but yes, used ones). B&H is still selling the body. Once their inventory is sold out, I'm guessing that that's that.
The nice thing about the GH- is that you can, with an adaptor, mount relatively affordable, used Canon FD lens. Wheatgrinder is one IT filmmaker who shoots with those, among other lenses. That's what I would do too. But what I don't have is a good wide angle lens that would work on the GH-.
It's been a long while since I watched Ebay for FD lenses, but hopefully they're still readily available. If you're willing to spend a little more, I do recommend trying Adorama's used department. I've had good experience buying a couple (a 24 and an 85, both beautiful) FD lens from them, and you're probably more likely to get quality and honesty/full disclosure from them, as opposed from Lord know's whom on Ebay. Not that you can't get lucky on Ebay, too.
What I think I would want to get for that (a nice wide angle lens) is the Olympus 12mm 2.0 lens. But that's an 800 dollar lens. But I sure do like the look of the videos shot with it that some have put up on Youtube and Vimeo. Those videos look better to me than the ones shot with the SLR Magic 12mm, for example.
I'm sorry. I've tried to research it. But I can't seem to find a lens that will give you a nice wide angle (one that I personally like, as in like that 12mm which gives you the look of a 24mm) on the GH2 that is affordable
and really good looking (to me, at least). I'm sure that the cheaper ones, like the stock lenses, are at least passable. But once you start comparing video (on the tubes) from them to video from lenses like the mentioned Olympus, well...
But I don't know. Hopefully someone else can help you (us) out with a good option in the wide angle department.
But look at some SLR Magic video on the tubes. It's fine to very nice looking indeed. It just looses when compared to the Olympus, for my taste.
I'm not assuming that that's a certain difference between the lenses, rather than "user error," or something.
I think there's a lot of love for other micro four thirds lens that can get you a nice wide focal length too, like one or more of the nicer Panasonic zooms, but they come at a steep price as well (er...depending upon how affluent you are, or are not).
Also, if I ever get to actually purchase one (the Olympus), one thing that would give me pause is that apparently it is a tiny lens. Is that a problem for focus pulling? Or would that even be much of a concern, generally, when you're trying to get your wide shots?
And, I haven't really looked up video from any of the other and more expensive alternatives to date, for whatever that's worth. =P
You find yourself in the company of Gh2philes here. Well, that's a bit of an overstatement. Canon still has a few lovers on IT too. Maybe they're just a little less zealous?
The thing about the GH2 is that it has hardly any moire. Also, in the US anyway, pretty much unlimited clip length. That's important to me because I am interested in (the possibility, at least) of making documentaries or doing event work. What do you want to do?
And heck, if you believe them, some argue that DSLRs are on their way out --mirrorless is the future, in which case, if that's true, something to consider in terms of what lenses you want to invest in. Not saying that I buy that at this time.
Also, everyone's ga-ga about bit rates. And the GH- has them good, especially the GH3.
But there's really nothing wrong with the 60D. Except, I would suggest, the moire issues, which could be inconvient for you. It seems to be a fairly well liked camera.
Lori Grunin of CNET doesn't love the 60D...but likes it fairly well, I guess.
It may be a little dated by now. But has some appeal to me thinking that it might be nice for a backup stills camera. Are you concerned about shooting stills at all?
Also, it's dropped in price quite a ways. Another question I have about the getting one of Canon's APS-C 1.6x crop factor sensor cameras is: what lens is going to give me a good wide angle? I can't afford one of Canon's L zoom lenses that will give me a nice wide angle without also being ridiculously slow.
[Oh, maybe this one: Rokinon 14mm Ultra Wide-Angle f/2.8 IF ED UMC Lens For Canon. Just learned about it thanks to icba pictures and the Indy Mogul video he posted.

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Yeah, yeah, light the hell out of your scene with one of the slower lenses. But good lighting ain't cheap either.
My two cents. Apologies for any errors, omissions, or foolishness. =D