First impressions: CV or research statement?

The first impression is, ideally, when you first talked with a prospective adviser and/or researchers in the department or lab before applying. Some people have small interviews (such as by phone or Skype) before application time, and it varies by person whether or not anyone will have even seen a statement or CV before/during this process. This naturally varies by region and field, but this is not uncommon in the US.

Naturally this is not always possible, in which case you'll just have submitted an entire application packet and have no control of the first impression - so literally anything you submit with the package could be the first thing a member of the admissions committee sees.

The typical routine is that an administrative department (generally "admissions" or a "graduate studies" coordinator) collects all the materials and puts all the information into files. Admissions committees then generally split up the applicants into sets and distribute them to individuals on the committee, with usually 2-3 people reviewing each applicant. It seems this particular handling of the process is very common (I've heard it from dozens of people in different fields throughout the US).

The first read varies by committee member, and it seems that absolutely everyone has their own weightings and order in which they review packets. Some professors say they think the personal/research statement is silly and the first thing they look at is the reference letters. Meanwhile some say they look at the reference letters last, as they want to see what the candidates own words are and then only see if the reference letters agree with that image. Some people think the CV tells the true story, while others think the CV is little more than a laundry list and nutshell reminder of what's listed in the other materials. Some professors have been reported as saying "I only accept people I've already worked with in the past" so the application materials are really just there to make the bureaucrats complain less, and pre-selected candidates need to just not screw up too badly on anything.

So in the end, in writing your materials you cannot assume any proper ordering whatsoever - everything has to be suitable if encountered first, last, only, or not at all!