For ropes, I put most of mine in bags. I've got a couple of static lines/bull ropes that I don't have bags for and I just gasket coil them. One of my bull-ropes is in a daisy chain right now, as my shoulders didn't feel up to the task of coiling it, the last time I used it.
My throwline is kept in one of those collapsible cubes, although I'm not totally impressed by it. Whenever I get a new throw line, I tie it taughtly between 2 trees for a day, in order to get rid of the "memory" and avoid tangles. I then put it away carefully, yet it's often tangled to hell when I go to use it.
Yeah, I always put them on/take them off pretty close to the base of the tree. My Buckinghams are the old-school good ones, and I don't want to wear out the spurs by walking around in them.
That spur design makes them a little more comfortable in the tree IMO. I could be full of it and just imagining this, but a lot of the newer gaffs have a spur angle that put sideways pressure onto my knees. I think the newer ones are less apt to gaff out when moving around, but I'll choose comfort over that. Those Bucks are great for the cedars, redwoods, large pines, etc...my old man used these to climb redwoods years ago and they're my favorite for most of the stuff I do. However, the long, steep spur does make them a bit unwieldy on broad trees. That's the only time I break out those Kleins...I've even got another pair that has shorter spikes.
I was given 3 sets of new/never used linesmen gear a couple years back. Most of the stuff isn't usable for tree work, but at least the gaffs were usable.