Wow. This turned out way longer than I thought it would. Oh well – I’ve bolded what’s really important, although I advise you read all of it (painful as that is

).
TehYoyo, Thank you for the enthusiastic reply. Oh my! I am getting total opposite replies regarding DSLR and DSLM... I am totally split between both at the moment. Seeing that video up on vimeo made me lean a lot towards the GH2, though, and with that sweet price. But I care too about the stills. I want to ask you, what do you say regarding teh tip above on the length of the video shooting on the Sony A57, for example? Is it irritably short taht I need to stop every 10 minutes or so? Are there other cameras you know of DSLR good video and still?
Sure - no problem.
Mirrorless cameras (I've never heard the term DSLM before - dunno if it's a thing) are the latest craze - which isn't a bad thing. In fact, they're quite good. They produce high quality stills
and video and are compact and light - a lot of people don't like carrying around large dSLRs. I got my Sony dSLT (same as a dSLR for this particular discussion) because I didn't think I'd mind carrying it around - I can't tell you what I think as of now b/c I got it 4 hours ago in the mail (it's great so far, though

).
One counterargument against mirrorless is that, with any lens on them, they're still unpocketable, as their size markets them to be. You'll still need to wear it on your neck or carry it in a bag of some sort (
I'd recommend around the neck).
As to the video on Vimeo, you can capture that with any dSLR, from the Canon EOS Rebel T2i to the Canon 5d Mark III to the Nikon D800 (with uncompressed HDMI output) to the Sony NEX line to the Panasonic GH2.
In regards to time limits, if you're making your own short films, movies, webshows, etc,
you're really not going to go over 12 minutes, or even come close (or else you're probably doing it wrong). The only time that issue has come up in a discussion I've been in is when this guy wanted to record a lacrosse game continuously. Even then, I told him just to wait for a break to make a new file. Easy. My Sony A57 can record up to 30 minutes, by the way.
Quick note about stop times and uncompressed HDMI output:
Research Magic Lantern. Now, as a Sony owner, I don't use Magic Lantern and so I haven't investigated it in-depth myself. However, from what I do know, it's a firmware (the software/program that runs on your camera) that adds extra features to a camera that users want but can't get with the standard firmware. I do believe that Magic Lantern for all Canon cameras offers uncompressed HDMI output (which you won’t use unless you’re really serious, although it’s worth looking up to see what the big deal is). Also, it handles auto-stop times the same way as the Panasonic GH2 - when it reaches the limit, it skips 3 seconds (i.e. creates a new file) and continues to record. Judge how detrimental that is to your work w/ your own judgement. It might matter to you, it might not.
As for recommendations, I was in the same boat as you (although with a smaller budget) just a few days ago. I wanted to get a dSLR that could produce good images (I wasn't going to nitpick, though - I went into it accepting that all dSLR images were
good compared to what I had been seeing (i.e. point and shoot) and so that wasn't a huge issue, although features like 10 fps at full resolution pushed me towards Sony) and could record 1080p footage at 30 fps at least. I also had a few features that I was looking for (fully-articulating screen, good or cheap lens lineup, etc).
I ended going with the Sony A57 over the Canon T3i for a few reasons:
10 fps continuous shooting stills at full resolution. Seriously. Will I use it a lot? No. Probably not. But it's
so nice to have and listen to. Awesome. Go to Best Buy and compare continuous on the A57 and the T3i and you'll see.
60 fps at 1080p for slow motion (video). No other consumer dSLR has that feature.
There were a few other motivations, like being different (I like standing out, and since almost every single novice has a Rebel of some sort, I felt cool buying a Sony), wanting to use old Minolta lenses on my camera, etc.
My recommendation for you:
At this point, it really doesn't matter what you get. If you
really, really want the small(er) size of a mirrorless camera, I would say get the Panasonic or the Sony NEX of your choice (choose based on what features you want/price/etc). But, I would advise you to get either the Canon Rebel T3i (which I consider the "safer" choice b/c it's so established, more support, etc.) or the Sony A57 (more risk/reward I think). A few reasons:
1) Lenses. Lenses are infinitely more important than the body. See
for more.
2) Features/Expandibility. Just b/c of the larger form factor, DSLRs can do more or at least do the off-the-beaten-path things better
3) Larger sensor(like what Sekhar said)
All of that said (and if you’re this far, congrats!), keep in mind that, in the grand scheme of things, the camera and the lens doesn’t matter as much as the person who is using it. Put a newbie in front of a Canon EOS 1DX with a 24-70L, a 17L TS-E, a 50mm 1.4L, a 70-200L (a few of the nicest lenses that Canon makes), etc. etc. etc. and give a professional an iPhone 5 and I guarantee that the professional will take infinitely better pictures.
If you watched the 2008 Olympics, I’m sure you noticed the hype about the Speedo LZR Racer suit – it was supposed to go extra fast. I remember one person said something to the general extent of “I tested it. I threw it in the water and it didn’t move, so I guess I still have to swim.” The same is true of cameras. The camera is only the tool – you still gotta make pictures.