  The Einstein Telescope (ET) is a proposed third generation ground-based
interferometer, for which the target is a sensitivity that is a factor of ten
better than Advanced LIGO and a frequency range that extends down to about 1Hz.
ET will provide opportunities to test Einstein's theory of relativity in the
strong field and will realize precision gravitational wave astronomy with a
thousandfold increase in the expected number of events over the advanced
ground-based detectors. A design study for ET is currently underway, so it is
timely to assess the science that could be done with such an instrument. This
paper is the first in a series that will carry out a detailed study of
intermediate-mass-ratio inspirals (IMRIs) for ET. In the context of ET, an IMRI
is the inspiral of a neutron star or stellar-mass black hole into an
intermediate mass black hole (IMBH). In this paper we focus on the development
of IMRI waveform models for circular and equatorial inspirals. We consider two
approximations for the waveforms, which both incorporate the inspiral, merger
and ringdown phases in a consistent way. One approximation, valid for IMBHs of
arbitrary spin, uses the transition model of Ori and Thorne [1] to describe the
merger, and this is then matched smoothly onto a ringdown waveform. The second
approximation uses the Effective One Body (EOB) approach to model the merger
phase of the waveform and is valid for non-spinning IMBHs. In this paper, we
use both waveform models to compute signal-to-noise ratios (SNRs) for IMRI
sources detectable by ET. At a redshift of z=1, we find typical SNRs for IMRI
systems with masses 1.4+100 solar masses, 10+100 solar masses, 1.4+500 solar
masses and 10+500 solar masses of about 10-25, 40-80, 3-15 and 10-60,
respectively. We also find that the two models make predictions for
non-spinning inspirals that are consistent to about ten percent.
