Cheap Reliable mower would be an 90s to mid 2000s MTD made mower with the 2 blade 38-42" deck, CVT transaxle and OHV briggs vanguard. Kohler command equipped if you can find 1.
Be prepared to put a head gasket in a OHV briggs powered one and some tubes in the tires but other than that they are a very reliable cheap mower.
Those Aluminum cased single speed CVT trans-axles last 2-3x longer than the hydros or that era.
Stay away from the Troy Bilts, Husqvarna and Noma mowers and anything with a Hydro transaxle. They are prone to several steering problems, Junk Kohler Courage engines and weak hydro transaxles and weak frames that can crack and a whole slew of problems with the decks.
Something like this one. But I wouldn't pay a dime over $250 for this particular one just because it looks like it was kept outside. It says it has a new carburetor so I suspect that it will need a head gasket. Those 2 things go hand in hand on an OHV briggs.
This one isn't bad but priced a little high. 12.5hp briggs flathead CVT transaxle 38" deck with bagger and new tires, battery, blades and starter. Looks pretty clean.
Another one with flathead briggs and a bagger. And priced to high.
And another. This one is super clean. Not a horrible deal if it runs and operates the way it should.
Another clean example.
The old Square hood craftsmans with the 5 speed are pretty reliable if you can find one that doesn't have a billion hours on it.