I totally agree that the tool itself is only a very small sliver of the problem and I'm well prepared to fight the cultural battle of adding process to task management and communication.

My greater concern is picking a tool that won't buckle under it's own weight. I use Trello personally but from what I can tell it won't hold up well when a team starts throwing a lot of tasks into it. Basecamp seems to have a similar issue with not handling volume well. Basecamp quickly becomes unruly because of the sheer number of places where the same information can live although I will grant that with enough discipline that shouldn't be too big an issue.

Brightpod seems like an interesting option because it's almost identical to Trello but with multiple views to narrow the problem space depending on the goal you're trying to assess/accomplish. Asana is another top contender for me.