I have 3, and formerly 4, H&R Single shot 12s and 20s, they are all very good guns. One was as cheap as $80. They are very simple and reliable, sturdy and well built. Be sure to avoid the Topper Model 158 (kind of rare anyway), the front stock is purposefully easily removable, and I found it is less sturdy and more prone to wear than the standard ones held on by a screw. Hop around LGSs or go to a gun show, you should find one or ten of them.
They do kick pretty hard in 12 gauge, but BBs in the stock and proper hold fix the problem entirely. If you plan on wingshooting, just deal with the recoil and lose the BBs, they kill the balance of the gun in a swing, way too back heavy. For rabbits, coyotes, squirrels, and cardboard boxes it is worth the odd balance. Even with a weighted stock and good hold and fit, buckshot still makes your arm dumb and jiggles your brain a little.
In my honest opinion, you are better off spending a little more and getting the H&R Pardner Pump or chasing down a used Mossberg or Remington, I'm sure you've heard this before. But if you are on a minimal budget or just set on a single shot, the H&Rs are great. They are really easy to clean, and I have not had a single Fail To anything. They all pattern straight, but, as I said, the lack of a rib and lack of front and mid weight makes them mediocre wingshooting guns.
"I am wanting a rugged, reliable single shot 12 gauge for rabbit/squirrel hunting."
Get one or three or five. All my siblings and shooting friends love them too.
EDIT: My first H&R was the first gun I ever paid for myself, an upgrade from a .177 break barrel pellet gun, which had taken rabbits, racoons, a possum, and dozen of crows. I still have 2 break barrel, 2 pump, and 3 lever action air rifles that see occasional use, particularly when the school nearby is in session. Possibly of consequence, I bought an H&R Pump for $160 just 3 months after I got my single shots.