I received an offer to publish an article on one of my websites for a payment, obviously they want a link out of it. I suppose it would depend of the quality of the article and website that they want linking to. Is this something to avoid completely?
In effect, you are being paid for advertising their article. I think that you are on the right track to review the quality of the article and the website that it is linking back to, but if they check out okay, I don't see a problem with doing this.
Agree, this should not be an issue as long as the quality is good. How much should you charge them for an article? Guess this depends on your site's DA and other metrics. Well knowned blogger outreach services like Fat Joe charge their customers around $130-150 for 1 article with 1 link and you as the website owner should get your slice of this cake.
Go for it if their website is related to your niche. It may be a great opportunity to develop networking as well as getting a quality backlink.