My wife supports my bike hoarding habit too, which has it's benefits, but I'd probably have a lot more living space if she didn't let me buy half of what I want to buy
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I'd probably post in the "Wanted" forum here on Ratrod about the Sachs hub. Sometimes there are plenty of them on Ebay; right now I don't see any. It seems to go in spurts. Just make sure you specify that you want the coaster brake version (I'm assuming you want a coaster brake, anyways). These hubs are absolutely rock-solid pieces of machinery; they truly don't make them like this anymore. There is also a really good article online on how to overhaul these hubs, so you could theoretically keep this hub going forever.
However, because you said you want this process to be as easy as possible, you may want to consider buying a brand new 3 speed hub rather than a used one like the Sachs hub. Because, let's face it, if you're going to use a 40-50+ year-old hub, you should really overhaul it with some fresh grease first. And while three speeds aren't exactly rocket science, if you haven't done one before, they are a bit daunting.
So otherwise you two other options are:
Sturmey Archer SRC3:
Pros: It runs silently (most three speeds make a ratcheting sound while you ride; I hate that), you won't have to re-space your drop outs as much (only to 116mm).
Cons: You could get a Nexus cheaper, there isn't much documentation out there on servicing these hubs.
Shimano Nexus:
Pros: You can get one of these dirt-cheap from Ind_Chuckz on these here forums, they also have perhaps the strongest brake of any coaster brake out there (it's seriously ruined all other coaster brakes for me).
Cons: Makes a rather loud ratcheting sound, you'll have to respace your frame to 120mm.
Also, Sturmey Archer makes a wide variety of 3-speed shifters that are compatible with both hubs. I love their seat-post shifter; it allows me to run a three-speed hub without having a gaudy cable running all the way from my handlebars to my rear hub.
Getting a 3 speed on your bike should definetely be doable. If you're looking for simple, I would probably look into one of the modern hubs. Just have your bike shop respace the frame while they build you a wheel. Just make sure your frame is made of steel; I've heard some people say these Swindlers are steel and others say they are aluminum.