Yes, you could do this, but if you can't afford basic services, then the cost of DVDs for any period of time might not be the better choice. I would suggest you get a dvd player that hasd a usb port. Then you can copy the files onto a usb flash drive and watch them that way.
Something like this one would work great:
http://www.amazon.com/Philips-DVP5990-1080p-Upscaling-Player/dp/tech-data/B00158OJ9O/ref=de_a_smtdTo do the actual recording you would need a tuner card. You can buy one new for around $80. You would need one that has a digital OTA tuner like the hvr1600. You can also find them used. Finally you would need some pvr software like GBPVR to handle all the recordings for you.
www.gbpvr.com