Does it matter what order I play the campaigns in?

There's no benefit to playing the campaigns in a specific order. (Aside from the tutorial campaign, of course)

There is however, minor benefits from finishing the five "standard" campaigns before taking on the "final" campaign: since you must pick a hero from one of the finished campaigns for the final campaign, finishing more campaigns gives you a greater pantheon of heroes to pick from.

That said, there is nothing particularly relevant about beating one of the 5 standard campaigns before another.

Pick your favorite!