The VW Beetle -- and the Super Beetle -- have long had a reputation for decades of reliable running. Much of that comes down to the simplicity of the air-cooled engine's design; but simplicity can be a double-edged sword when it comes to maintenance items like oil.
Engine Oil -- VW's Advice
VW was very proud of its engine's anywhere-anytime reputation, and its popularity all over the world. Beetles were designed to be run through the snow on sawdust and moose urine; maybe that's why the VW owner's manual said of oil changes: "The VW engine makes no demands in respect of engine oil quality, which cannot be fulfilled by every well known and popular brand." That's very diplomatic of VW, but real-world, decades-long experience with these engines show that they definitely have preferences in terms of engine oil. Also not mentioned by VW is the fact that these engines, which lack an oil filter, require changes every 3,000 miles religiously.
From negative 4 degrees Fahrenheit to 77 degrees, a 10W-30 or 10W-40 will suffice. If you never drop below 0 degrees, you can use a 15W-40 or 15W-50, and 20W-40 or 20W-50 will suffice if temps don't drop below 14 degrees Fahrenheit. These air-cooled engines tend to run hot, so don't use anything thinner than a -40 multigrade. You can use an old single viscosity oil like an SAE 20, 30, 40 or 50, but it'll only narrow the oil's operational range.
The fact that the air-cooled engine lacks an oil filter really affects your engine oil choice. First, you'll need to use a "high detergent" oil that will keep sludge and soot suspended in the oil, and keep it from sticking to the inside of the engine. Some people prefer a heavy-duty diesel truck oil like Rotella T because it has very aggressive detergent packages that will keep the engine clean and happy, but a standard high-detergent automotive oil will suffice. If you're switching from standard to high-detergent oil, mix it half-and-half on the first oil change; you don't want all the sludge dissolving and breaking loose on one oil change. Don't bother with a synthetic. You have to change the oil every 3,000 miles to get rid of dissolved sludge, so the synthetic's ability to run 6,000 miles or more is wasted.