Asana - Easy for non-technical folks to grok, all the features I need for non-coding projects (like a marketing project for example)
Pivotal Tracker - More technical features specifically for software development, steeper learning curve, good bug tracking.
Slack - Good for office-wide communication. Easy to use for everbody.
Bugherd - Bug tracking system which integrates into the user-facing components of your web-app. Makes gathering feedback/bug-reports from the public very easy.
Do you use a special methodology (agile/scrum/timeblock) and need something to fit that or are you running your project ad-hoc?
If it's a case of the latter then I would advise to look into adopting a methodology and a systemized way of working before locking yourself into a tool.
In my experience there is a big correlation between using a methodology and having a solid foundation to build a solid business.
It is really worth looking at github if you have not seen it lately. There are some big project running on it. There also newer product that are tightly integrated, like https://www.blossom.co/kanban-with-github
I'm using Zenhub at my current company. I preferred Pivotal Tracker, which we used at my last company. It just feels kind of janky overloading Github's website.
TBH, though, I struggle to find any other meaningful negative differences.
We use JIRA at work, and there are good and bad aspects.
My biggest peeve is that management always want to configure it to do time-tracking. This makes engineers hate the tool and lie to it, making it useless for bug tracking.
Pivotal Tracker - More technical features specifically for software development, steeper learning curve, good bug tracking.
Slack - Good for office-wide communication. Easy to use for everbody.
Bugherd - Bug tracking system which integrates into the user-facing components of your web-app. Makes gathering feedback/bug-reports from the public very easy.