It is easy to say "shoot it with this camera or that camera," but it really depends on a few things.
1. Your budget (rental is a good way to go)
2. the look/quality you want
3. your filming style
4. the skill of your crew
DSLRs and 4K RED cams are great if you have the budget, the supporting rigs to get the shots you want, and the skill of the crew to get it right. It's impossible to get good shots by handholding the camera, and movie full of static shots are boring. Usually you would need a portable sound recorder too, so you can get good quality audio.
If your budget and crew are limited, but you can still afford to go this way, I would rent a Sony PMW-EX1 or EX3. The camera works very well as hand-held. You do not need to worry about lens costs, it's a very good Fujinon built-in lens, the camera is very practical, and its 2/3'' sensors still give a pretty good shallow DOF, not as shallow as 35mm. I think it still looks great for an indy film. You get 1080/24p with XLR inputs, and you can get away with no steadicams or Zacuto rigs.
I would rather watch a well-filmed production on an EX1 than a shaky, boring video from a 5D Mk2 where every shot is the amateur film maker trying to show off the shallow DOF. In Hollywood movies, those shots are rare anyway. It's only noobs that do that and tell everyone how "Hollywood" it looks.
So, rent an EX1 or EX3 - the only difference is the EX3 is more ergonomic (which is a good thing).
Rent a good 3-point lighting kit.
Rent a Sennheiser 416 with a boom pole.
If you can do all your filming in 1 day, this will meet your budget. This requires good planning and time management though. Some places may give you the same deal for a whole weekend, so it's worth calling around.