Making Pepper-Flavored Vodka
From my limited (but successful) experience, here are some answers to your subjective questions:


Choose peppers whose flavor you do want
Avoid peppers whose flavor you do not like (I'd never infuse green bell pepper, blech!)
Choose a vodka you'd want to drink (if you like cheap vodka, use it, if you like expensive vodka, use that)


As far as the mechanics of making the infused vodka:


Chop the peppers up coarsely, drop into a glass jar with the vodka, taste every 12 hours until you get the flavor/heat you want, then strain the vodka.  
The longer you infuse, the stronger/spicier the result.
If you're going more for flavor (less for heat) remove the seeds and pith
The proof of the vodka (80-100) will have little difference in the end result as far as the infused flavor goes.  Everclear (190+ proof) will probably extract flavors faster, but do you want to drink it????


If, on the other hand, you are really just wanting to get the spiciest drink available, then don't bother infusing vodka, just google how to get/make capsaicin concentrate and use that directly.  Then add directly to the drink of your choice.

I've not tried dried chilies, but I imagine a Chipotle infused vodka would make an awesome Bloody Mary.