Hey,
I used to own the DT 770 Pro 80s. I believe it was the 32 ohm version. They are extremely comfortable headphones and sound excellent, but they are very bass forward, which may fatigue your ears overtime. I know it did for me.
I would recommend looking into V-Moda headphones. I have an older pair of closed-back V-Modas, wanna say the Crossfades M-100, I use at my office desk and I really like them. Their build quality is excellent, they have removable single-sided headphone cable, nice well-balanced sound, and some of them come with hardshell cases and external mics (if you use with your phone). The Crossfades are smaller and sit on top of your ears, but they have larger models that go over your ears as well. Look around, V-Moda definitely has some in your budget.
Then again, if you can find the DT770s for $125, that's a great price. Just be prepared to potentially use your EQ to drop the bass a bit.
As far as cable length, Grado makes an excellent extension cable for headphones. I own and use this one.