In order to receive all the TV Essential channels (both SD and HD) requires the Advanced TV Package and an HD Set-Top-Box or renting a CableCARD.
http://ww2.cox.com/residential/tv/prices.cox
Advanced TV is an additional $3/mo added to the Essential Package price
Renting a Box from Cox:
An HD Set-Top-Box from Cox is $8.50/mo (probably the Cisco 4642HDC or SA 4240HDC)
Retail CableCARD devices:
You could also rent a CableCARD, from Cox @ $2/mo (the SDV Tuning Adapter is provided free)
Then purchase the Samsung GX-SM530CF Smart Media CableCARD Set Top Box
http://www.amazon.com/Samsung-GX-SM530CF-Streaming-Player-Built-In/dp/B00EYO241Q
Another option would be to purchase a used TiVo Premiere with Lifetime Service on eBay they are currently selling for $300-$400. Many TiVo customers have upgraded to the new TiVo Roamio, that is why there are so many for sale.