I would recommend either a 700d (t5i) with magic lantern or a 70d (which will hopefully get magic lantern soon), Canon 600d T3i if on a budget but it can only do 960×540 24fps raw vs 700d 1280x720 24fps raw (using magic lantern), they both do 1920x1080 24-25-30fps H.264.
Keep in mind that the camera and lens is just a small part. You also need to factor in a microphone, tripod, editing software, possibly external HDD (video takes up a lot of space), SD cards, Colour accurate monitor, more ram (after effects loves to eat up ram) and possibly a Steadicam rig or Glidecam rig. That being said what are you planning on shooting with your camera? Short films are a very broad term. Action? Drama? Documentary style?
My recommendation. Assuming your tight budget I would go for the 600d (t3i), along with this (in order of importance)
1. 600d with kit lens 18-55mm (good starting lens, good range, Optical stabilization),
2. Camera bag (just buy a cheap one, don’t need anything fancy, like $10)
3. Tripod (can get a decent one for about $50)
4. Microphone (do not skimp on audio). I would recommend the Rode Video mic Pro (it’s about $200). (your better off getting a cheaper camera with a separate dedicated microphone than an expensive camera with no microphone)
5. Canon 50mm F1.8 lens (they cost about $100, should only use it on a tripod though as it has no stabilization and is a semi-long focol length)
6. Lights (buy some spot lights, or something like that for indoor or night shooting), and some deflectors (refractors)
7. Rode smartlav+ (make sure you get the + version, this can be very helpful for getting good audio, plugs into your smartphone), they’re about $60
8. Green screen ($20), this really depend on the work your doing.
9. Editing software (premier pro/after effects, Film riot has some good cheap editing software tips on YouTube I believe) probably about $100
If you still have budget left than I would recommend jumping up to the 700d if possible, given that it can do higher RAW resolution video (using magic lantern).
Here is a good video on audio gearhttps://www.youtube.com/watch?v=HM-dTyTeCes&list=LL8wlxNfLxFp2oGhkXihsJH...
Also what are you planning to edit on, not all displays are colour accurate. This is a cheap display but still good “Asus VS248H”. if your budget dramatically increases you can Pick up a 70d with a 18-35mm f1.8 sigma lens and a DNA 5050 steadi cam along with a NTG2 microphone and an external H4n recorder (because NTG2 direct in camera sounds bad)