A few weeks ago I lucked into a dirty but otherwise really nice S&W Model 18. I detail disassembled, put it in an ultrasonic, got nearly all the gunk out (still some buildup on the bottom of the top strap but I'll take care of that when I clean it today I think)...and finally got it to the range yesterday.

The first cylinder was some generic stuff, the 2nd cylinder was CCI Stingers, the 3rd cylinder was CCI MiniMags, and after that...everything got really sticky. I had to beat on the extractor to punch the brass out; it was not getting pressed out at all without a good bit of force. After a couple more cylinders I called it a day. I don't know if the Stingers pooched it or what, but it was not happy.

Anyway - is this normal? What can I do to prevent sticking like this? I really don't want to have to carry around a soft mallet with me every time I decide to bring it to the range

Not unusual.  Depends on the condition of the chamber reamer when Smith made the gun.  A lot of people chase the cylinders with chamber reamers.  In my case, I used a couple 22 cal chamber mops and some Mothers mag polish chucked in a drill on my nickel Model 34-1.  My 18 is fine, but the 34 stuck like a mother.

It took out the rough surface and ejects cleanly now.

Maybe someone was popping .22 shorts in it. Spin them out with a cleaning brush or run some lead remover cloth thru each chamber.

I have 17's 18's 34,s all older and none are sticky until you run a bunch of ammo. My Ruger SP101 4'' is far worse in that respect.

Compuvette is correct. Go over to smith and Wesson forum and do a search, hundreds of posts regarding this. Smith revolvers have notoriously tight chambers, and most will recommend picking up a finish reamer and cleaning the chambers up to solve the problem. As noted above sometimes polishing without reaming is enough.
Ammo type plays somewhat of a role ( generally CCI is considered best of the domestic makes, steer clear of Remington and Winchester ,federal is a coin toss)
But it is a very common complaint

I used Fltz on a barrel mop spun by a hand drill to polish the chambers of my S&W model 18.   Polishing really helped my model 18 which was manufactured in 1958.   I tend to mostly shoot plated 22 LR ammo and these days either Aguila or CCI.

Ok, whew, at least it's a "known" issue...I'm guessing that was why it was put up for sale in the first place

Mine's an older one, IIRC early 50s? There's some crud that needs to be basically scraped off on the top strap right above the barrel, but it doesn't seem to be "harming" anything so I'm not going to do much beyond finding one of my brass AR brush things and trying to dislodge stuff there if I can...the cylinder itself is clean; no buildup anywhere, no lead, nothing - when I got it I brushed the hell out of it then put the cylinder in an ultrasonic bath; it made it squeaky clean.

I honestly should probably break out that brush either way - when I took it to the range, after a couple of cylinders the cylinder itself was a little rough. It would get bogged down shooting in DA; trigger pull would get really tough until it rotated into place. Forcing it by thumbing the hammer worked but I got the gun to practice DA in the first place I saw there was some buildup on the face of the barrel, or forcing cone, or whatever the correct term is - but I didn't think it was too bad...and after cleaning it's as slick as can be, maybe it's just at the cusp of being too much. I'll brush that out some more and see if that helps, too.

If it's marked as a Model 18, it's no older than 1957. Prior to that, it would have been known as the K-22 Masterpiece 3rd Model.

It's pre-18, K162xxx - according to https://www.smithandwessonforums.com/threads/s-w-model-change-information-links-to-help-find-what-youre-looking-for.170946/ this post on an S&W forum, 1952

Very nice, Ed.

That looks great. Mine is an 18-3 which appears to have been built in 1975.

Thanks guys - I lucked into it; it's got some scratches on the left side above the trigger and some marks on the right side, nothing major - it was dirty though. If I had to bet, I would say it was a farmer's gun; I'd bet the scratches were from a button inside a holster or something like that, and it probably went wherever the farmer couldn't lug a 10/22 with him. I'd also bet the farmer passed, one of their kids shot it some but had no idea how to clean it so it got gummed up, and since they didn't know dick about guns decided to sell it. They had no idea what it was worth so they consigned it for basically nothing.

I didn't want it, but at that price...if I didn't buy it, someone else would have. It had been there a day when I saw it. The only reason one of the guys behind the counter didn't buy it himself was, to quote him: "Well...what am I gonna do with a 3rd one"

Have you tried just limiting yourself to 18 rnds per outing?  

For all the reputation of the 18, I suspect the vast majority of them rarely average more than 18 rnds/year.

Beautiful revolver! The “proud pin” front sight variation wasn’t made for very long.
Again best answer is hand finish reaming cylinder, but as also mentioned you might get away with a slight polish of the chambers.
As you might know, the hyper velocity 22’s like stingers use a slightly longer case and may give you more trouble.
These guns are built like tanks.
The last model 17 I had  ( same gun essentially with a 6” barrel) had tight chambers also. It would start sticking after maybe 75-100 rounds though. A quick few passes of a brass brush in each chamber ( just dry no solvent) every 100 rounds or so would keep it running just fine. I put at least 100 thousand rounds through it and when I sold it, was still tight as the day it was built