that looks like a mechanics tool bag.
https://www.amazon.com/Rothco-G-I-Type-Mechanics-Tool/dp/B000BFNJEI
Here is what I use. I take my 08 WK Hemi on the beach, air down from 33 psi to about 13-15 psi. It takes about 2 minutes per tire to get back up to 33 psi when I leave.
Hose & cord is plenty long, however I bought a 6 foot hose extension just in case.
It gets hot, I bought a nice canvas bag to keep it in, I've had no issues with the heat besides accidentally touching it and getting a little burn.
Compressor - http://www.amazon.com/gp/product/B005ASY23I/ref=oh_aui_search_detailpage?ie=UTF8&psc=1
Extension Hose - http://www.amazon.com/gp/product/B00ELJD0BW/ref=oh_aui_search_detailpage?ie=UTF8&psc=1
Bag - http://www.amazon.com/gp/product/B000BFNJEI/ref=oh_aui_search_detailpage?ie=UTF8&psc=1
I have the 88P and am very happy with it. I towed my 5th wheel on a 9000 mile cross country trip and it got a ton of use with zero issues. I bought this bag to carry it.