This year I'm planning on applying to some number of physics graduate programs, and hopefully set myself on track towards a PHD. I'm having some difficulty determining what "tier" program I should be applying to because I have a somewhat lop-sided application profile. I provided a short outline; I feel that I could easily improve my GRE scores a few points before applications are due, but my lack of relevant research, non-physics undergraduate study, and expected weak recommendation letters may be holding me back significantly. I've seen statistics on average scores or GPAs, but I feel that those alone can't really describe what odds I may have.
Put succinctly, if I was able to push by PGRE score up in the 800s do you think that my application would be taken seriously even with other sections lacking? What might be an example school or two to illustrate what types of programs I might have have some probability of getting into?
Ga Tech: BS Mechanical Engineering (2012), GPA: 3.15 (junior+senior years), 3.78 (sophomore+freshman at Georgia Southern)
Research Experience: Essentially nothing, had a senior project which could loosely qualify as an equivalent
Work Experience: Energy Engineering, Controls Engineering
PhysicsGRE: 760 (64%), MathGRE: 700 (61%), GRE: 164, 155, 3.5