Pretty much agree with this, though there is a more expensive model of the K240 which has better bass response to my ear.
Bass response is tricky. We like to hear bass when we listen to music, and as bassists we need to hear it well. But many headphone manufacturers do punch up the bass because that big bass sound sells headphones.
The problem is that, for mixing, you want something that isn't hyped, because hyped does not equal accurate, and accuracy is critical for mixing and monitoring. So the real question is whether or not you can get one set of phones that's going to meet all your requirements. I'd say mixing/monitoring and what most people perceive as good bass response* are mutually exclusive, unless by "good" you mean "accurate."
If accuracy is the goal then my personal preferences are the AKG240 Mk II or the Beyerdynamic DT770 80 ohm. I own them both and either one will work for you. AKG is semi open, the Beyerdynamic is more isolating so if you'll be tracking anything with open mics while wearing them the Beyerdynamic is your better choice.
*Please note the qualifiers and let's not argue about good vs. accurate vs. what most people want. I've sold hundreds of pairs of headphones.