If you have the fund go straight to prosumer and don't look back. Unless you are also taking photos, a DSLR for filming is just way too limited. The sensor, power, and recording caps are not video friendly. You pretty much have to install custom firmware just to make the DSLR video usable and that's not ideal.
Personally I use a 7D to film with a set of L lens, but if I was solely shooting video I wouldn't have pick up the DSLR.
Ive used DSLR's for filming for the past year or so. Ive never had any issues and much prefer them to camcorders TBH.
The sensor and the power have not been an issue whatsoever. There isnt a recording cap either - well never for the ones I have used. Because of the card format used there is a limit of 4GB file size, but the camera just creates a new clip and continues recording, so you just place them together in your editor for seamless video.
I mainly shoot video only. My previous Canon EOS 650D (Rebel T4i) was great, and my current EOS 70D is even better as it autofocuses like a pro camcorder.
Personally I would say go with a DSLR with a decent kit lens, which should be more then enough for the OPs needs. This is YouTube remember, how much sharpness do you really need, considering YouTube's compression algorithms will always affect your end video quality anyways.[DOUBLEPOST=1379450013,1379449827][/DOUBLEPOST]
The 60D is a great camera - it's what I shoot on. I even use the kit lens - which is a little slow, but gets a clean shot and even zooms a bit.
The main thing you'd need to consider is recording length. The 60D has a shot time of 12 minutes before it times out. Which will make filming long format events, concerts, or plays impossible in a single take.
A prosumer camcorder can be a bit more adaptable, but there's a lot of decent budget equipment designed for DSLR shooting.
Check out cheesycam.com for some great tips, reviews, and links!
Ive not had any time limit issues with my 650D, or with my current 70D. Yes, it'll limit file sizes to 4GB, but continues to record and splits the clips, which you edit together later for seamless video. I know they can only record up to a certain time limit (I thought it was 30 mins or so?) as otherwise its no longer considered a camera, but a camcorder, and has some kind of tax implication making them more expensive etc, but Im pretty sure it continues to record and just splits clips.
I'll test on my camera later
The 70D is speedy fast - just like using a camcorder. The AF really is buttery smooth and FAST. But you also have the added flexibility of changeable lenses, which is why I prefer then over camcorders - oh and the easy to use MOV file formats rather then AVCHD formats!