Do you need to keep the episodes for an extended period of time, or would it be just so that you can watch them later?
I would recommend using a DVR. It wouldn't matter if you subscribe to DirecTv or Comcast; both companies have reliable DVRs. If you don't need to physically remove a VCR tape or DVD disc and watch it on another television, then you may wish to explore this option.
Not sure if you know much about a DVR, but basically it works like a computer. You don't have to set it to certain times or channels, but you tell the machine "Record all Grey's Anatomy episodes" and it does it. You won't have to update it every week, you can save them as long as you want (typically) and if the networks ever do the funky garbage they like to do such as making the program 64 minutes instead of the normal 60, it automatically records all 64 minutes and you don't miss the ending. Also, if you have a DVR that has 2 tuners, you can record 2 programs that are on at the same time (I like Dancing With the Stars and Heroes...they're both on at the same time and I can record both of them).
I have a DVR and I absolutely LOVE it. It took a little bit of getting used to, but once I got the hang of it it was easy.