What type of pump is best for compressing gases for a compressed gas cylinder?

A positive displacement pump, of which there are several.

Piston or Reciprocating pump.

Axial sliding vane, or even a Wankel pump, (the engine in reverse), named after its German inventor.

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It is called a compressor, usually distinguished from pumps since pumps handle liquids. For this application, a reciprocating compressor (which uses pistons) or an axial compressor (like a turbine in reverse) would be called for, depending on the pressure and volume.