Not knowing what you already have or have access to, in the way of lighting, mics, external audio recording, tripods/camera cranes, dolly track, "Steadicam" or similar worn stabilizer, vehicle mount devices, cables, and all the other stuff that goes in a production, it is difficult to know. As well, while Final Cut will be a fine editor - we don't know which Mac you are using.
You have two options...
1) go the dSLR route. The interchangeable lens system can easily get you to the DoF you require. Shooting a movie usually means lots of short scenes and takes, so the video file time limitation of a dSLR capturing video does not matter. Your big issue is fast action - and highly compressed video generally captured by dSLRs compress lot - and high compression capture + fast action do not get along well.
2) I suggest something around the Sony HDR-FX1000 or maybe HVR-Z5. You can get good DoF by properly using the manual aperture and shutter speed controls, and the DV or HDV format this prosumer can record is low-compression. For what it is worth, the original "Paranormal Activity" was shot with an FX1000 (or a HDR-FX1).
All can do 24p frame rate (or even electronically derived 24 frames per second).
In either case, this leaves budget for lots of accessories.