I found it really nice and easy to tandem them at the hospital (and ever since), I didn't use my EZ pillow until maybe the last day or so (4 nights there). At first we just raised my bed so that I was sitting up-ish and pilled pillows and rearranged for a little while until it seemed comfortable and right, the babies basically nursed football style, but splayed out a little (I could work on their latch a little better that way). I had nurses show me the first time, got one attached, then the other. It was nice having so many nurses around to look and say "good latch" and for extra hands those first few tries, and I was able to figure out how to do it. My DH was able to stay with me the whole time and he was a tremendous help with holding one or the other if one woke and the other was asleep. They had a basinet that held both together, so we learned how to swaddle and put them together in the basinet (although they weren't very sleepy until they were attached an with me lol).
Now as for REST... rest? never heard of it.
Well, there was this really nice nurse who took them twice for us (2 different nights) to try to get them to sleep, rolling them around, in the nurses stationm while DH and I tried to get some more restful sleep, other wise I slept with them on me (pretty comfortable, and nursing makes you sleepy too) or if they happen to sleep in the basinet.
Oh, and the boys were born ON their due date, so no nicu time, or tiny mouths to deal with.
I would recommend the EZ pillow at the beginning, unless you have a C-section, you might not be able to position yourself (get up) well enough, but after several days you should be more able to.