You're correct: The Winchester 120 is the budget version of the 1200.
They are very smooth shotguns. The 1200/120 replaced the iconic Model 12 and, of course, were never able to measure up to their predessesor in the minds of most sportsmen (just like the post-64 Winchester rifles vs. the pre-64s). Nevertheless, they were good shotguns, IMO. I've had a 1200 for 30 years, used it hard, and never had any trouble with it whatsoever. Wouldn't trade any of my Model 12s for another one, but my 1200 has been a good gun. The barrel looks factory from here. I have a second, "riot", barrel (and factory marked as such) that looks exactly like yours...exact same sights, and it's just over 18". One other thing about the 1200 that I like is that it is extremely easy to break down completely for cleaning*.
For $175, I think you did well.
*Just be sure you understand how the ejector fits on the ejector retainer pin on the inside of the receiver.