As the saying goes 'invest in the glass, not the bodies' - and I would have to agree with it. You will probably switch your body every 3 to 4 years, whereas good lenses should last 15 years +.
I really don't think the Canon Rebel line is up to the task you want it for - I'm not sure about the T3, I've never seen it but if it can't shoot native ISOs like the T2i can't, forget it. The 60D is a good entry level body and i'd start with that, I would encourage eventually a 2nd body (for both safety and 2 camera interviews) so if you eventually get a 5D, you won't have to throw out your 60D, you'll still get a ton of use out of it. As far as people talking about better or worse 'autofocus', you really have to believe me that in the video world, autofocus is never used, so any kind of 80 point autofocus argument is simply not applicable to what you are wanting to use it for - and 'servo zoom during shooting' don't get me started on how useless that feature is.
As far as lenses go, Unlike most 'pro' video cameras, which essentially have one 24 - 500 mm lens (and a wide-eye adaptor you can pop on the front), that's simply not an option in the DSLR video world for anything decent quality. So eventually, you will need several lenses. But to start I would say either the 24-105 f4 L or the 17-55 2.8 IS if you plan on shooting lots of handheld. The advantage of the L series is the build quality & if you eventually get a FF body it will be very useful with that, the drawback is you don't have a wide lens (38mm on crop camera) and in video you really do need that option. The advantage of the 17-55 is you do get that wide angle you will need and you get a 2.8. The Disadvantages of this lens is the build quality, no weather proofing, limited focal range and you can't use it on a full frame camera down the road.
I do a ton of handheld shooting so IS is really essential for me, as is a good viewfinder like Zacuto (part of your budget?) but if you think you won't be doing much handheld I would recommend an L series 2.8 like 16-55 or something so you can use on any future camera. You get great build quality, your wide angle but not much telephoto - but I still think you're wide options are more important initially than your telephotos - in some cases you can move closer to get your nice portrait CUs etc, but you can't back thru a wall to get a wider shot.
Also, since you want to do docs and lots of interviews you are going to need approx $2K for the audio gear you need although pro most sound guys would even scoff at that number saying that's what they pay for 1 mic. I in no way mean to get preachy, but most people new to video greatly underestimate the importance of getting good sound.
If you have the best lit/looking video but crappy audio, your interviews, and therefore your project since interviews are the backbone, is useless. But if you record great audio and you leave the lens cap on, you could still create a great doc. from the audio and b-Roll cover. So you really
need to budget that into your kit - you'll need Mics (more than one type for different situations), headphones, XLR cables, boom poles, windsocks, & external recorder(s) - I always travel with 2, explaining to client that your interview is not usable because your $200 recorder broke after they've flown you halfway around the world and put you up in hotels is not a conversation I want to have - luckily good microphones like good lenses should last over 15 years, one of the AKG shotgun mics I use is over 20 years old and still sounds fantastic. Don't scrimp on the headphones either, if there's a buzz or hum in the room because you're crossing your audio cables over AC cables or getting wireless interference from PA systems or cellphones you won't hear it with iPod earbuds - again, hearing that can take seconds to fix on set but missing it can ruin your entire interview - which of course you won't realize until your in the edit suite - it's not just your time (& maybe clients money wasted), there are moments you capture in interviews you can never re-create a 2nd time even if that particular person did agree to let you do it again.
Sorry went long on the audio note - but since you're not getting into video to shoot HD stock or music videos, I'd say get a T2i and a used $100 50mm 1.8 lens if it means you otherwise can't afford decent audio gear for your interviews (or hire a sound person) - Good luck!