I'd go with the 6'8" wide for sure. Just a little more comfortable for most everything. As far as length goes, you should be fine with a 16' if you don't have a whole bunch of cows and don't very often haul them around (from one pasture to another). I have a 24' x 6'8" Circle D, and I just recently sold a 16'x6'8" WW (pulled it a lot for 2 1/2 years, never spent a penny on it, and was offered $1000 profit on it - sounded too good to turn down at the moment, but now that I'm trying to buy another one, I'm not so sure). I pull a trailer 3-5 times a week typically, and at least half of those times are longer drives with just a few head. I love a 16' for those kind of hauls, just easier to get around tighter places with, but I know most people don't do as much of that as I do.
As far as swing/slide vs. butterfly gates, it mostly depends on the kind of places you usually load out of. If you load out of alley's, it's by far easiest to just use a slide - you can just open one butterfly there, but you have to open it to the inside, so you have to be in the alley to close it, and if you have a full load or just cattle trying to come back out it can be difficult and even dangerous. On the other hand, if you load out of wider gates, butterfly's are nice because you don't have to be as exact in backing up - just open a gate to either side and they take up the slack for you. With a swing slide you have to (barely) bump the left corner of your trailer to the gate post, being sure you have room to get your gate open, and swing it to the right. I prefer swing/slide myself, I know many that prefer butterfly's.
The one thing I won't buy is a single swing gate with no slide -guess those are mostly meant for horses, but you sometimes find them on stock trailers. Matter of fact I drove a couple of hours to look at one that looked great in the pics (regular center gate, not horse dividers) but never actually showed the back gate. Lesson learned - ask if you can't see it. I never even thought about it not having a slider...