I just want to purchase ~200 copies of my anthology containing short stories and sell them to family and friends by myself in order to donate to charity. I don't need an agent. I can format by myself and all content has been edited. I just want copies of my work bound.
You don't need a publishing house for that (and anyway your intended distribution is too low for such companies to be interested). You just want to self-publish your work.
When I self-published a book (making, ultimately, about 300 copies), I went to a commercial duplication place that could do production and binding. I was producing a manual, so 8.5x11 photocopied pages with a comb binding were fine for my needs and I used somebody like Staples or Office Depot. If I instead wanted printing and bookbinding I'd probably still start there and ask for a referral if they can't do it.
There are also online options such as Lulu and Cafe Press. You upload a formatted, edited copy of your work, choose what kind of paper, binding, etc you want, and can then order printed books. These options tend to be pretty expensive, as they're also selling to people who want 5 or 10 copies, but their options and prices are oft-changing so it's worth checking the currently-available services.
I think CreateSpace is a good candidate for this. The cost per copy is better than photocopying, and it will be nice perfect bound paperbacks. This route will also allow you, if you choose, to make the book available for sale online through Amazon and other outlets, with you getting the net proceeds to donate as you would personal sales. There are no setup fees, you just pay the cost per book.