Headphones feel and sound different to each individual. Either try them out before buying or make sure they can be returned.
I use Shure SRH440.
Sennheiser HD280PRO or Sony MDR7506, recommended by u/Dr0110111001101111, should work well too.
• Hard Case for traveling with it.
• RCA to XLR cables because the DDJ-400 only has RCA outputs and he wouldnt be able to plug directly into speakers with RCA.
• Good headphones that aren't Beats By Dre
• Small Portable SSD hard drive with ample space for music. Avoid HDD as they are disk based and you can lose all your data if dropped.
I do not remember that talk, however Giantbomb's go to headphones for there podcasts are Sennheiser HD 202 which are only $25 the only issue with them it that the audio cord is over 10 feet long.
The headphones that are used in the control room are the Sennheiser HD 280 Pro at $99 which are great headphones for the price.
And if you can find a pair the Sennheiser HD 419 which I use are awesome I have a large head and I can wear this for hours on end without issue. They go for about $30 - $40 if you can find them.
Sennheiser HD 202 - https://www.amazon.com/Sennheiser-202-Professional-Headphones-Black/dp/B003LPTAYI/ref=sr_1_1?s=aht&ie=UTF8&qid=1484144599&sr=1-1&keywords=sennheiser
Sennheiser HD 280 Pro - https://www.amazon.com/Sennheiser-HD-280-Pro-Headphone/dp/B00IT0IHOY/ref=dp_ob_title_ce