Now that Fall 2016 applications are wrapping up ... Time to start thinking ahead to Fall 2017?

I'm planning on applying to grad (PhD) programs for the fall of 2017, which gives me about a year (to be safe, let's say 9 months) to prepare and put together my application.

So I guess my very general question is ... How?

Programs I've been looking at (incomplete list):

• CUNY - (applied) mathematics, partly because it's near friends (I did my undergrad nearby), also because they sent me an email telling me I should apply (which is a good sign, right?)
• UC Berkeley - operations research, partly because it's nearby and I wouldn't have to move
• University of Louisville - systems science, mostly because my former research advisor is the head of this program

Background:

• Math and physics double major at a top tier private university, class of 2012 (still paying off loans -_-), 3.15 GPA (ugh)
• 1 year teaching math at a public high school via a Teach for America-esque program
• Misc IT and software engineering experience
• MS in math at a not-so-well-known university (basically part of a big state university system), 4.0 GPA, graduated in 2015
• Worked as a research assistant at a data mining research facility while doing my MS
• Currently working as a data analyst in SF

Areas of interest: Applied math, data science (yes, I know they're two very different fields ...), to a lesser degree computational physics

Application specific stuff:

• Took the general GRE in the fall of 2011. I had no prep or any idea of what to expect when I went in (bad idea), but I managed to do decently--161 verbal, 168 math, something for writing (Does it matter? I don't remember what I got, but I do remember I did terribly because I didn't bother writing more than a paragraph since I heard most universities don't care about this portion of the test).
• Terrible math GRE score. Similar situation with the general GRE--no prep going in. Score: 670 :( Should I retake?
• I'm pretty confident my stats professor from my MS program is willing to write me a good recommendation. My research advisor from my MS program is MIA at the moment, but I'm sure he's willing to write me a good recommendation if I can track him down (he left the school right before I graduated). Do I need a third recommendation? I'm not in touch with any of my undergrad professors--hopefully I can make good connections at my current job, maybe?

Issues:

• I have no clear/focused course of study. My background consists of a bit of pure math, a bit of applied math, a bit of physics, a bit of statistics/ML, etc. Right now I'm torn between applied math and data science. And those two fields are very broad--they can fit into the math, physics, CS, stats, OR, and engineering departments. I also have always been a generalist, which is why I chose math and physics as my majors in undergrad (the "most general" sciences).
• Related to the above: no clear idea of which schools I should be looking at, which schools I'm qualified for, etc. But I guess this is just something I have to research (I'm also completely outside the academia loop).
• Poor grades from undergrad, but since that's was a few years ago, it should be okay, right? I have a 4.0 from my masters program, but the school isn't as high profile, and it's a masters program--everyone gets straight As.

So anyway, since I'm trying to get a head-start, what should I be focusing on? Is it weird to randomly email professors about a paper they wrote years ago? Should I retake the GREs (in which case I need to study)? Any recommendations for other programs?