Neither chore jacket.
On headphones, avoid Bose and Beats. If you're using them for gym wear, I'd go with something really lightweight and cheap. I personally dislike in-ear buds unless I'm flying, but most people don't have problems and they're good for the gym since they isolate.
For a smaller closed pair, I love my Senn HD-25. Built like a tank. I've been tossing them in my backpack for years and they're still in mint condition. Audio Technica makes decent pairs too (M50). I don't recommend moving up size-wise for any sort of portable use. You'll have to make a whole portable rig with a separate headphone amplifier, and honestly it's just a PITA and not worth the effort. Whoever recommended Grados for portable use, don't listen to him. I love Grados, I have three pairs, but they sit on my desk. They're completely open (let sound in AND out) and will be uncomfortable if you wear them snug enough to walk around with.
For home use, I'm all for ridiculously big cans.