Applying for specific assistantship vs general PhD program (and other questions)

[mayanway]

I'm planning to apply for PhD programs next year (for a Fall 2014 start) and am just starting to research my options. I'm discovering that I know very little about the graduate school application process, so please forgive me if these questions are overly basic. Some background: I'm a recently graduated veterinarian hoping to make a career in research focused on "One Health" concepts - particularly on factors that influence transmission/spread of infectious disease within wildlife populations. My actual course of study will most likely be in ecology or epidemiology, and I will probably focus on programs associated with veterinary schools. I spent most of my school breaks working on wildlife research projects, but wasn't sure that pursuing further study was for me until a few months before graduation. I'm currently a small animal vet and will continue to work this job until I am accepted.

I routinely see announcements for graduate assistantships on specific projects. Some of them are extremely relevant to my interests and background. I'm curious whether there's a major difference between pursuing one of those opportunities vs simply applying to a PhD program within a department of a particular school. I suppose the advantages would be guaranteed funding if accepted, knowing your lab/advisor from the start and potentially being able to start work on your project earlier in the curriculum. Disadvantages might be less flexibility to pursue a project of your own design. Anything I'm missing? Any implications for program "prestige" or employment opportunities post-graduation?

My other questions pertain to the general application process and funding. My understanding is that people typically apply to a program within a department at each school and that funded positions are typically reserved for more competitive applicants. Are you typically notified of your funding situation when you receive your acceptance to the school, or does that come later? Does in-state vs out-of-state factor in at all? Is it an entirely different situation for a US citizen applying to programs abroad? Can you be committed to a particular lab at the time of acceptance - and is that typically established simply by contacting a POI prior to the grad school application?

Two important factors for me are that I end up in a program with a significant field research component (ideally where my DVM degree is relevant) and that I don't accrue any additional educational debt. In that vein, I have seen multiple threads where people mention that outside employment is forbidden - how common is that, and does it apply to school breaks as well? I understand that most grad students don't have much time for outside work and are still in the lab when the undergrads are off, but relief veterinary work could potentially be a nice secondary income source on an "as time permits" basis if allowed.

Thanks to anyone who read through all of that! Any input is appreciated, and in the meantime I'll continue perusing the previously amassed knowledge in old posts