Thanks for all the tips, advice and observations so far. I am starting from a position of complete ignorance, so everything is helpful.
One tip is to wrap it in foil and stuff it in a Coleman cooler with a bunch of towels. This will hold for at least two hours. Actually, I always aim to try to finish early and let the meat rest in this way.
Since you mentioned you already have Weber grills, which I assume are typical kettle-style, you could get a ‘taste’ of the smoking experience by looking into the America’s Test Kitchen recipe I mentioned upthread, without having to buy a smoker first.
Watch the video. If you think “I think I can do that” follow the recipe. Maybe you’ll end up saying, “eh, the results were good, but too much work for me”. Or maybe you get hooked, and then you invest in a fancy new smoker, and start coming into threads like this giving your expert smoking tips 
Good tip. I had never even eaten homemade smoked meat, so I used our barrel-style charcoal grill to smoke some chicken. It was rather hands-on. But the result was very tasty, and convinced me I’d love the results if I could get a solution that wasn’t quite as difficult to keep at the target temperature.
I’ve had a few different types. Didn’t like the flavor from the electric, and it only lasted a year before the element burned out. For years, used a vertical propane smoker - IMHO ok for flavor and ease of use, but a pain to clean. I currently have a charcoal offset but am finding longs smokes on that to be a chore in terms of refilling the firebox without getting too much smoke from the wood or charcoal and playing with the dampers to maintain the best temperature. However, the flavor seems best. A typical bin of charcoal and wood will last about 4 hours, and since cold meat absorbs smoke best I do all of the smoking up front, then finish the meat in the oven as it’s easy to maintain proper temp and no further smoke is needed.
It should be noted that there is a lot of leeway in the temp. I use a Weber Smoky Mountain and I never check grate temperature. I do check meat temperature from time to time to get an idea of how fast things are moving along. Now, I admit, I have a lot of experience smoking, but even when I started I didn’t use a grate thermometer. As long as you’re anywhere from 200-about 300, you’ll be fine. And if it spikes briefly, no big deal. I tell myself that home smoked flavor comes from the temperature fluctuations. 
Point being, people stress and get a bit too neurotic about being exactly at 225 or whatever. You’ve got room for slop. It’ll come out okay.