Paper
From my experience, paper and envelopes can make a big difference. Human nature is human nature, and it's just natural to reach for something nice before something plain, and to subconsciously put a little more stock in someone with a more professional manner. Especially with a query. A query is as much, or more, about the writer as about the story, and selling yourself will often get you further than trying to sell words on paper. How you come across matters.
The idea is to get an agent to look at your manuscript, and how you present yourself can mean as much as how you present the story. Agents and editors see hundreds of good queries, but request manuscripts from only a few.
It is the writing that matters, but it's naive to think it's always and forever the only thing that matters, and it's naive to think the medium can't hinder the message. First impressions matter, as well. And sometimes a yes or a no is determined by who gets opened first, not by who was better.
In the job market, it's supposed to be skills that matter, but try going to a job inteview without showering or shaving, and wearing ratty clothing. Few would do this, even for a position in the back room where the public will never see how they look.
It's easy to say don't obsess, but when it's said too many times for too many things it soon becomes laziness.
And two things I can absolutely guarantee: 1. You do not have to obsess in order to use good paper and good envelopes. You simply have to reach for it next time you go shopping, and be willing to pay about two bucks more for a fairly large pack that should last months and months. 2. In no way, shape, or form will using good paper and good envelopes harm your query at all, ever, in any way, so why not use it.
Your manuscript will have to sell itself, but a professional query letter, one that looks professional, that tells an agent or editor you're willing to put a little money where your mouth is, that you take writing seriously, can make said agent or editor ask to see your manuscript, and that's what it's all about.