If you have Tivo and subscribe to netflix you just scroll down to the bottom of the shows you have recorded there is a Netflix button. The first time you do it they have some info you fill in, after that you just click on the button. It brings up the list you have prepared on the netflix site. That said, we find that there aren't nearly as many things we want to see there as you might think--most of the new stuff comes as dvds rather than streaming. Lots of older things too--we are working our way back through The West Wing and it is strictly dvds. Some things come and go according to their agreements with different companies--we used to be able to get As Time Goes By, for instance and it now is back to dvd only. I actually keep meaning to cancel that part of the service--not worth it for us. (Note to self....). I would recommend going to the netflix site and browsing to see what is available on the streaming service before signing up to see if it is worth it for your tastes. I do not know about ordering single showings of things and paying--that is available thought several sites but I've never been in such a rush that I couldn't wait for it to come on Netflix.
Oops--just reread your original question and saw that you asked about amazon--never have used it. I'll leave this in case anyone wants to know about netflix.