Ask HN: Setting up an affiliate program?

I'm spinning up a marketplace site for plants (http://doleaf.com), and we'd like to offer an affiliate program.

We had it on our long-term roadmap, but recently found a site that's such a perfect fit that we want to bump it up and push out a basic program now. The owners of the other site are eager to integrate our listings, so we want to get moving quickly.

What's a good way to go about setting this up? We want to offer a % of the sale price, but don't want to deal with sending checks, managing analytics, or anything like that. Is there a 3rd party service that will handle all that stuff? I'm imagining some kind of service that handles redirecting to us, keeping track of who sent us the traffic, and sends the check. In return, we just get a monthly bill with the affiliate fees.

Anyways, I'd love any sort of advice on setting this up.