It depends on the fuel and the machine, but generally empty tank and carburettor is the best advice.
If the really expensive fuels are used (£15 per gallon - over three quid a litre!) sold for the express use in small engines, the tank could be left full.
Apart from that, the tank and carburrettor should be completely empty as the modern day fuels both (1) contain ethanol and (2) rather more of the volatile fractions are included.
Alcohol is hygroscopic and will attract water. When the larger fraction of lower alkanes evaporate, the fuel will be ‘stale’ and the engine may not start or run properly.
Winterising, by adding oil to to the cylinder(s), to line them completely, is a good insurance plan. Spark plugs should be replaced and the engine turned over until the piston (of single cylinder 4-stroke engines) is on the compression stroke so that both valves are closed to avoid condensation within the cylinder. Same with 2-strokes, but either inlet or outlet port will be open, wherever the piston is postioned.
The situation (with all cylinder valves closed) cannot be achieved for twin cylinder engines with 360 degree crankshafts, but could be for those with 180 degree cranks.
Engine oil should be changed at the end the season to remove any acidic residues which are collected by the oil during the running season - engine internal components will be better protected.
For engines with the modern type of carburettor, follow the instructions - usually they specifically state that leaving fuel in them is only OK if it to be used again within a month.
For multiple cylinder engines it was often advised to spray an oil mixture into the inlet manifold as the engine was switched off, allowing the internals to be coated with an oil film as the engine slowed from fast idle to stop.
Of course, as the poster indicated, the tank should either be full or completely empty, never part-filled, to avoid condensation problems. A plastic sheet fitted under the fuel cap can be advantageous if the cap is a vented one.
I have a diesel generator, so the fuel issue is lessened, but the tank is always full, ready for action, if required.
Engines should never need replenishing with oil before starting - a recipe for a potential expensive failure, unless the engine is fitted with a low oil level trip (and that may not be fail-safe!). Especially so, if it is dark at the time!
Also, generators should be run periodically, to lessen the likelihood of poor starting, when required, and to avoid any damp in the windings leading to an elecrical failure.
Hope that clears up up some of the issues. Better than just posting a ‘nothing post’ as in post #4.