Here's my subject, a well-used US Engines 41cc gasser. It's well used, but the price was dirt cheap. Including purchase price of the engine I'll probably have it running for less than $70. If I wanted to make my own carb mounting gaskets and re-use the carb isolator it'd be closer to $55. Some "optional" stuff will be done on it as well while I'm at it.
The first thing I did was to give it a general once-over. It's very dirty, but I can see the piston and don't see any scoring or other black-flags. Since the plug was installed I rotated the propshaft counterclockwise and verified that it has compression. I then pulled the plug and rotated it some more, listening and feeling for any issues. None were found.
Checking out the carb there were a few issues. First, it's dirty as heck, the mounting bolts (well, a bolt and a screw) don't match, and the throttle linkage is bent/broken. I pulled the mounting hardware and confirmed the two pieces are the same thread pitch, so that's just a cosmetic issue. The broken linkage is no big deal, it's a homemade piece that will be replaced. The throttle itself works just fine, opening and closing the intake. It's also got a Walbro carb, so I know the rebuild kit is cheap.
Here's a very important step in determining the health of the
victim subject - does it spark? This is easier on a magneto engine as there are no extra bits of electronics or batteries needed. With the plug out and the plug boot/wire attached, ground the plug body against the engine and turn the flywheel/propshaft. FAST, where the magnet passes the magneto, and if all goes well you'll see a spark at the plug. Note that you've got to turn it fairly quickly to see a spark - faster spin = better spark. To do this on an electronic ignition engine you need to power the ignition module. This engine passed the spark test. Part of the rehab on this engine will include a new plug wire, plug, and plug boot. I'm not a fan of the pliers scars on the propshaft…. Those will be cleaned up a bit as the work happens.
The engine came with an aftermarket Bennett muffler. They're loud enough to wake the dead, kind of negating the word "muffler".

This is also a smoke muffler, although one side is capped with a bolt. It's also got a little leaking around the outlets. The plan is to clean it all up and re-seal the outlets to keep from making a mess on the plane it eventually powers.
The magneto isn't the cleanest one I've ever seen, but it works. The terminals will be cleaned up and I'll need to do something about that corroded wire coming out the top. When inspecting an engine, take a BRIGHT light and shine it between the cooling fins! When I first looked at this engine I thought there were cracks in the head, but the light let me see it's all just casting marks. Note that a couple fins have slight bends, but no fins are broken and there is no sign of physical damage (is neglect physical damage?). The engine is missing the prop bolt and washer, but I've got spare parts to take care of that.
Soooo, the engine is rough, no doubt about it. But it's cheap and it'll be a fun project. Now that I know it has a good foundation I'll make up a shopping list of "needs" and "wants". I'll also pull the carb and get that cleaning started, as I am pretty sure I've got a rebuild kit for it.