I use Lightroom and Photoshop. Just my personal preference, as editing software is yet another personal choice with lots of good alternatives out there.
As Don mentioned, Photoshop is expensive and IMO unless one knows why one wants it, it isn't necessary.
BTW, Adobe has recently gone the subscription/cloud route re Photoshop. Far as I know, it is no longer available for outright purchase anyway.
IMO, yes, post processing is important when using a decent DSLR, arguably more so. I regularly use images as is from my compact point and shoot, almost never from my DSLR's. But again, that's just my opinion and the way I happen to do things. No rules, personal choice again.
If I had to choose one and only one piece of software, it'd most likely be Lightroom. 5 - 10 years ago, it would have been Photoshop.