What and who grades your "first" impression when you start a new civilian job? Is it the recruiter, your new boss, or someone/something else?

By the time you "start"? I'd say your boss and your co-workers. By the time you start, your recruiter's job should already be complete.

You will make several "first" impressions:
-Your initial supervisor will form a first impression within a day or so of you joining his part of the organization (very important)
-Senior managers will form an impression based on welcoming meetings (if they do this in the organization) or after checking with your supervisor during the first few weeks of your employment
-The HR and other support specialists will form a first impression of you in your first few hours on the job. (these folks have a lot of power, so it's a good idea to be on their good side)
--You co-workers or team members will form a first impression of you during your initial interactions with them. Some will see you on your first day, others may not see you for a week or two depending on the type of work. Good impressions foster team work and mutual support.

I recommend, be polite, humble, and positive throughout your first few weeks on the job. Realize you probably don't know much about the real jobs of the people you meet. You'll have to listen, learn, and eventually you won't be the new person.

For the group I work for, it's the team. We don't hire based on how well the managers like you, but how well you fit into the team.