Practice with the bag you will use!
About ten years ago I got a throw bag. (after theBob convinced me of its utility, though I'd never really needed one in many many years of paddling prior. But then I hadn't often paddled water as small, swift, complicated as what I was beginning to do.) Thinking I might on some unforeseen future occasion want to use the rope to pull a stuck boat out, I got a 70' 7/16 one. I practiced with it in the yard for quite a while, finding a strong underhand throw to give me the most distance and accuracy. I got to be OK with it. I carried it around for many years but never had occasion to use it except as a camping pillow.
Then two years ago at Canoecopia I saw some 1/4" 70'ones at a good price and figured I'd get one that took up less space, was lighter and therefore (I thought) easier to throw. A month later a situation arose where someone got caught in a strainer, tipped, got out, and swam to the opposite shore. I was going to throw the rope over and haul them back to their boat.
That lighter bag went in trees, fell short, got caught in wind, went every single where but the where I wanted it to go. It was like pitching a whiffle ball for distance. Well, I hadn't practiced with it and it surprised me. Don't do that. Its embarrassing. I've since discovered overhand, like a football, works best for me with that bag and I've since practiced that way.
Practice doesn't have to be a grim "do or die" thing. If you ever take kids, nine or ten year olds, on summer paddles I've found most kids that age love to swim, pretend they're drowning, and have a bag thrown to them, and get hauled in as fast as you can. The faster the better. In playing that game you may even find you get more practice at their request than you really thought you needed. Multiple throws without repacking, fast recovery, repeat asap.
For rethrows I bring the rope in in 6' (armspan) lengths. Loops for the first half of the rope go on an upturned left palm (for righties), on combined index, middle, and ring fingers for the second half of the rope. Comes in fast and feeds out pretty smoothly that way.
Being a canoe guy, I carry mine clipped to a thwart just in front of me. I don't take it most of the time on my home river - flat, sandy, and with few strainers - unless I'm paddling with strangers or those whose skills I really don't trust much. Even then, if I were to need to do a rescue it would likely be by offering a grab loop and paddling them in. If I forget the bag in the back of the truck, as I sometimes do, I often don't make an extra trip at the put-in to get it. But in swifter water, with large groups, when its cold, paddling with strangers, its always there on that thwart just in case.
Good things to have but, like so many things, useless without practice.