When doing field recording for film, there are two things about the recorder that I would not be without, and that is good limiters, and low-cut filter, both preferrably analogue to prevent distortion in the input stage. These are things that many lower cost recorders, like the R-44, does not have (they all have digital ones as it's cheaper). This is one reason a mixer is often recommended, though more professional units like the 702 or 722 usually has this built in.
Secondly, as tonedeaf says, reliability is vital. Film is extremely expensive to make, and if by buying a more expensive but reliable piece of gear you can prevent a failure or some technical problem that takes up valuable time, you have most likely saved in that cost.
Another thing to consider, is how many channels you need. Many simpler, low budget jobs can be done with two channels, especially with a 302 mixer where a boom can be on one track, and two lavs mixed together for the second. Some higher end multitrack recorders, like the SD ones, do not have preamps for all channels. In these cases a mixer can again be good to supply this.
Also consider that in the long term, good microphones and preamps may last you 10-20 years, but a recorder (unless it's a more expensive, professional one) tends to be more prone to development and new investments.
Are you going to be working alone, or have a boom op? (assuming you are the mixer as you stand for the equipment) Then you need to think about how to get monitoring for him/her, and if you are going wireless or not. Once again, a mixer would provide, or a wireless reciever with a headphone output.
Do you think you will need timecode? If so, then the cheapest alternatives are HD-P2 (cannot generate it though), 702T, and R-4 Pro. These are all good recorders, but the SD is better built than the others, plus the others does not have the limiters or low-cut.
So, a mixer together with a cheaper recorder (not the H4n though, there are better for the price), or a 702/722, would probably be the way I would go, unless you need more channels.
I would advice you to also get a hypercardioid for interiors, as shotguns can sound a bit ugly with lots of reflections. Maybe an AT4053, since thats probably the best you can get for the limited budget (the Oktava MK012 is a popular low-budget choice, but is very prone to handling and wind noise, so I wouldn't recommend it if you can afford better).
Questions like this is common at dvxuser.com, so you can check there for more recommendations.