The excitation of Alfven and fast magneto-acoustic waves in coronal loops driven by footpoint motions is studied in linear, ideal MHD. The analysis is restricted to azimuthally polarized footpoint motions so that only Alfven waves are directly excited which couple to fast magneto-acoustic waves at later times. In the present study a periodic driver is applied at one end of the loop. The effects of a more realistic random driver are studied in the companion paper De Groof & Goossens (2002) (hereafter referred to as Paper II). The first part of the paper is devoted to the study of resonant absorption and phase-mixing in the absence of coupling (azimuthal wavenumber k(y) = 0). Since the density varies across the loop, resonances occur at the magnetic surfaces where the driving frequency equals the local Alfven frequency. In a second part where Alfven waves with k(y) not equal 0 coupling to fast waves are taken into account, we find that the behaviour of the MHD waves is strongly dependent on the driving frequency omega(d). Especially driving frequencies equal to a quasi-mode frequency seem to make the difference. The fast waves excited in these cases are global oscillations of the system and form quasi-modes as they are damped through the resonant coupling with Alfven modes. Since these resonances occur at the same location where the original Alfven wave peaks, the resonant peak is further amplified. While in most cases coupling has a negative effect on the growth of the directly excited Alfven waves, driving with a quasi-mode frequency leads to a faster growth of the resonant peaks and a more efficient decrease in length scales than in the uncoupled case.