I am no expert. I've only sold one domain, privately. I got a few tire kickers over the years for various domains I owned, and just moved on. I would have held out for more than $1,000 in your case. It's a good name. Problem is it's tough for a small startup business to pay what it would be worth. My buyers were starting a pretty capital-intensive business and $3K was a drop in the bucket. They are no longer in business, btw, and the domain has been for sale for years, with no buyers. The price was once well over what I got, but now it's $1,495. I guess I was lucky. But I knew by their first offer of $1K that they at least were not just hoping I'd give it away. I went way higher ($5K) but made it clear I was negotiating and expecting a counter.
I don't know about a broker. I've heard they only want high-ticket domains. I'd gladly pay them a percentage if they can get me a better price than on my own, but the question is, are mine high enough value? Your case might be interesting because it could be a great name IF there is a well-funded startup, that a broker can find.