Perhaps others had a different experience, but I was surprised at how many schools I got into in the top 20 and, overall, I think I under-shot things. Definitely apply in the top 25. Hell, apply in the top five and see how it goes. Have a couple back-ups where the fit is perfect and your stats are competitive, and maybe you'll get a great funding offer in case it doesn't work out with higher-ranked schools. My stats were very similar to yours (same GPA, quant score was 780 but 680 is still in the very good range). This seems like an intimidating process--but just don't sell yourself short or you'll be disappointed.
As for contacting profs, I always followed this:
1) Intro sentence: hi, I'm so-and-so, I graduated from this school in this year and I'm applying this year
2) Couple sentences about my interests
3) Your research looks exciting--would you mind telling me what you're currently working on and whether there's anything cool going on in the department?
4) Here's my CV (I found this to be key because it legitimizes you, use PDF format)
All the profs I e-mailed responded quickly and were quite helpful.