In this paper (the first of a series) we describe the construction of fixed-point actions for lattice SU(3) pure gauge theory. Fixed-point actions have scale-invariant instanton solutions and the spectrum of their quadratic part is exact (they are classical perfect actions). We argue that the fixed-point action is even one-loop quantum perfect, i.e. in its physical predictions there are no g2an cut-off effects for any n. We discuss the construction of fixed-point operators and present examples. The lowest-order q overlineq potential V( r) obtained from the fixed-point Polyakov loop correlator is free of any cut-off effects which go to zero as an inverse power of the distance r.