The following email was sent to a client who is researching project management tools. After writing it, it occurred to me that it might be helpful to others researching similar PM and collaboration tools. Feel free to chime in with comments if you have constructive information to add to the discussion, as I'm not an expert on any of the apps mentioned in this post.
After sending the Slack link to you, I noticed that the list of integrations for Slack is currently more pointed at software developers than anything else, so I'm not sure if it's the right tool for a publishing concern like yours. Still, it might be appropriate.
You mentioned that you are looking at Basecamp, but that is a different kind of tool. Basecamp isfor project management, whereas Slack is meant to integrate existing tools (including Basecamp competitors Asana, Jira, and Trello) to make collaboration faster and smoother.
For project management we use Jira, an extremely powerful (and proportionately complicated) application that is geared mostly toward software and web development. I would not recommend Jira to your company, as I think it's too complicated and not designed for the kind of PM you need to do. By the same token, I believe that Basecamp is too non-developer-oriented for our company and does not provide the agile management tools that Jira does.
While Basecamp is still not on Slack's list of integrations, Jira is, which is one reason that Slack looks like an appealing app to use. If you really think you want to use Slack and you're open to consideration of PM tools other than Basecamp, Slack has existing integrations for Asana and Trello.
We used Trello before moving to Jira six months ago and were generally impressed with it. It's a very simple and effective task manager that turns what are essentially glorified to-do items into structured lists on topical boards for ease of tracking and management. It's a lot like using post-it notes on a wall to track progress, but more sophisticated. One big advantage of Trello is that it's free. The main reason we left Trello is that it was too basic for us. We needed an app designed for agile management with the ability to control task "flow" through the system in order to make sure that issues don't fall through the cracks, as sometimes happens on Trello if you have lots of tasks.
Asana is a head-to-head competitor with Basecamp that you may want to consider, if you haven't already. I recommend googling "Asana Basecamp review" to compare/contrast them.
If your mind is set on using Basecampe, there is potential for using Zapier to connect Basecamp and Slack, but be sure to research it thoroughly before you go that route. In the past I've found integrators like Zapier and IFTTT to be too rudimentary without API access to the features we really wanted to customize. IFTTT allow two apps to talk to each other, but their abilities to go deep enough into the apps to access the data you want is limited, and they proved to be insufficient for our integration needs in the past.
There is a home-grown integration called Slackcamp on Github "which finds new activity from Basecamp and posts it to a specified Slack channel." I don't know if it provides enough detailed access to the APIs to make it worthwhile, but you might want to look at it.
Finally, there is a new service in beta (by invitation only) called Cloudpipes that claims to be able to "pipe" data back and forth between the two apps. Intriguing, if it works.
Good luck with your search for a better project management system. I hope you find this information helpful.