For an OTA DVR... Tivo has you covered. Unlike the tablo above, this has free lifetime channel guide service.
https://www.tivo.com/shop/detail/roamio-ota#/roamio-ota
Watching other shows I don't have a clear answer for, but...
You can cut your cable bill by a good bit if you're paying for boxes. TWC was getting my dad for over $70 a month in modem/dvr/box fees. What I planned out for him was $80 for a modem, saving ~$7 a month (this can be $15 if you're paying for home wifi BS server, just get the same wifi modem for $110) and the modem pays off in less than a year.
For cable boxes, the Tivo Roamio series. You get one box, 4 or 6 tuners, that records all of your shows. The Roamio plus is 6 tuners, $320. No need for the pro, it just has a larger HDD, you can add up to 2 USB hard drives to the plus. For each tv that you would like to watch live or recorded TV, you get a Tivo Mini. It's as full featured as the DVR box, and you connect it by either coax or ethernet. $120 a piece.
Only remaining things here are a cable card rental (like $2.50/month) and tivo service. Tivo service you have two options. $15/month, or $500 upfront lifetime. For my parents, the cost of all the hardware here vs the savings w/ lifetime tivo subscription had them gain a box and a payoff period of about 2.5 years.
Bonus: the boxes aren't the lagging hunks of shit that TWC/WoW give you, and they have built in support for netflix/hulu/plex.