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A good rule of thumb is the maximum useful magnification factor equals 50 times the aperture diameter in inches. So if you see a telescope advertising "540x" but its aperture diameter is only 3 inches, they're simply lying to you. This scope's maximum usable magnification is about 150x.
Aperture is especially important if you're looking at dim, deep-field objects.
Advertising a telescope based on its magnification power is a little like advertising a car based on its maximum speed. It's meaningless. Saying a 3" scope will magnify 540x is like saying a Kia will go 300 mph. Well, perhaps it can, if you drop it out of an airplane. But a Kia will never do 300 mph on a normal road on its own power.
Besides, nobody buys a car based on how fast it will go, because the maximum 75 anyway. With telescopes things are a bit more flexible, in that the maximum useful magnification is dependent on aperture size.
I recommend a minimum of 3" aperture for a good, general-purpose catadioptric (or Cassegrain) scope. If you buy a Refractor, you can get away with slightly smaller aperture since Refractors inherently gather more light per inch than the other kinds. If you buy a Reflector (a Newtonian or Dobsonian), go larger than 3" because they're inexpensive. Spend your extra money on more aperture!