Why are you welcome? Because after reading this (lazy) post, you'll know more about coaster brakes than roughly 100% of the world. Thanks to Jim on BikeForums for the info -
First off, for normal riding, almost any reasonable coaster brake can be made to work fine. If the brake is less than 20 years old, it's most likely a KT (Kun Teng) these are/were sold under the Hi-Stop, Shimano, KT, Suntour, and other names. They are cone-clutched brakes as were most of the coaster brakes made since the late 1800's. I don't know if you saw these drawings I made a while ago but they give an idea of how this type of brake works. If you want more of an explanation I'd be happy to give it. There's also this 'how-to' using a middle of the road Bendix brake. It might help to look at this and the drawings together to see 2D and 3D (sorta') representations of the parts and how they fit together.
The lever that attaches to the chainstay is the brake arm and is used to prevent the non-drive end of the hub from rotating. Basically, what your're doing is creating a friction connection between the hub and the drive-side cog while pedaling and a friction connection between the hub and the bicycle frame (via the brake arm) while braking. It naturally follows that there is no friction connection to either frame or cog while coasting. Look at the drawings and the position of the cone-clutch in those three modes.
The brake on my Rodriquez and my steamroller are Velosteels made in the Czech Republic. I have a nifty slotted, stainless tab welded to the chainstay of the Rodriguez to secure the brake arm. The Velosteels are a really nice hub when properly greased and bearings (cones) adjusted. Sadly, they come from the factory virtually dry of grease so they need work before they are ready for use. The Velosteels are pretty much impossible to get in the US right now which is sad. It's based on a 1904 Sachs design and is not a cone-clutch design but uses a roller-clutch (see my avatar to get a rough idea of this mechanism).
Regarding the best hubs to buy. I'm partial to older German (Sachs, Fichtel & Sachs) hubs. Sachs designs/patents were also licensed to companies like Renak, Perry and Excel so those are nice too. Another slight variation is the Musselman hubs (sometimes branded as Higgins and Elgin). Of course we can't forget the Bendix which range from really nice to reeeealllly crappy. The older units had hub bodies fashioned as a single piece (no pressed-on flanges) but a properly maintained Redline (redband) is a good useable hub. The last hubs bearing the Bendix name were made in Mexico and these are very low quality .... not worth using in my opinion. They're clearly marked Made in Mexico on the brake arm. I would avoid the Blueline (blueband) hubs as well. These are all cone-clutch except (as mentioned) certain models Sachs hubs that were roller-clutched.
Another sweet hub is the Sturmey-Archer SC-1 but they are very hard to find. Penultimately, the Cadillac/Rolls-Royce of hubs is the Morrow. These are really sweet but are quite complicated and require a tricky adjustment, during assembly, to work properly. It's not likely you'll find one lying around anyway. In fact, the reason the slot is so long on my Rodriquez is to accomodate the longer arm of the Morrow that I am slowly rebuilding.
Finally, the New Departure brake, like the Bendix redline, are the easiest hubs to find. New Departures were the first real coaster brake made (1896) and are cone-clutched but they do not use brake shoes like all other coaster brakes. Instead, they used a stack of disks like a motorcycle clutch to provide the braking action. From a design point of view, they're really nice but for braking action, many feel the leave alot to be desired. I have a few of them but have yet to lace one into a wheel to try it. After reading old articles about the early Repack race, the general concensus seemed to be that ND's always burnt up half way down the mountain and that Morrow and Musselman brakes were preferred. But for normal riding they may suffice.
Remember, coaster brakes (like all friction brakes) stop by converting forward motion into heat. Because the braking is done in a small area (inside the hub as opposed to the circumference of a rim), heat build-up can be extreme especially if the brake is used alone during a long decent. For this reason I would suggest adding a front brake to any coaster braked bike unless you live and ride in the flatlands.
So what's the practical differences in all of those brakes I've listed? Mostly in the amount of drag the hub exhibits during coasting and pedaling. Some hubs like the Sachs use a spring clip to actively retract the shoes while others simply allow the shoes to rest on the inside of the hub. Morrows actually 'disengage' the braking mechanism at both ends to reduce drag and the Musselman hubs use a split cycinder shoe to achieve the same type of shoe retraction as the Sachs and Morrow. The roller-clutched hubs have less drag as well. But for all practical purposes, the drag in any hub is acceptable if it is well-lubricated and adjusted. The only hubs that I feel are rediculously draggy are cheap Joytechs and Mexican Bendix hubs.
There's also the 'smoothness of braking' properties too. That is, how 'linear' the braking action is between slight braking all the way to lock up. Brakes that lock up with too little back-pedal force are undesireable. Most of the brakes I've listed do well enough in this area.
Caveats: Marketing departments being what they are, some hubs aren't necessarily what they appear to be. For example, Morrows were made by Eclipse Machine Company which was purchased by Bendix in the mid 1920's. Many years later when Schwinn decided to release a classic fat tire cruiser to commemorate some anniversary, they purchased the coaster brake from Bendix. Bendix, whose entire brake production had, by then, moved to Mexico, thought that it would be a great idea to give the brake a classic feel by stamping Morrow (in it's classy script font) on the brake arm (they did own the trademark).....travesty! I have seen these lowest-of-quality brakes for sale as Morrows. Beware. Back to Schwinn for a moment, Schwinn used coasterbrakes from just about every manufacturer out there. Most of the time, the brake arm is stamped with the words 'Schwinn Approved'. Some of these brakes are superb (like Sachs) and some are not (like the fake Morrow and Mexican Bendix) so you can find gems here but be careful. A German hub should have 'Germany' stamped on the body and would likely have an oil port on the side of the hub too.