RE: Original vs. Mini Co-Sleeper
We have the mini, and it was plenty big for us. My daughter slept in it until she was a little over 4 months old and she's quite tall for her age (over 90%ile). It folds very compactly and is easy to travel with in the car (I didn't fly with it so I can't comment on that). I used the sheet it came with, I thought it was fine but I also used a sleep positioner most of the time she was in there and also swaddled her so she never came into much contact with the sheet. It seems soft enough to me, though. You can purchase sheets that fit it that would be softer, and I've also heard some people use pillowcases tucked under, which I think would work well, too. The mattress fits very snugly so it wouldn't be a SIDS risk I don't think.
Also, FYI if you are leaning towards the mini and want another option, when we flew home when DD was about 9 weeks old MIL bought the graco travel-lite crib and it was pretty much exactly the same size as the mini cosleeper. The only difference is that the side doesn't come down and it doesn't attach to the bed. I never attached my cosleeper to the bed as DD was never mobile when in it and it didn't seem necessary, honestly as much as I love our cosleeper and will use it for the next baby, for less than half the price I would have gone with the graco if I did it again. But, at the time we bought the mini, I was desperate for something that could fit against my bed and in my postpartum desperation I just sent him to BRU for the cosleeper without doing much research!
Best of luck!
M, mommy to A 2005, E 2007, and L 2010