Released in 1997 the OM2000 was not actually built by Olympus but instead by Cosina. It is a camera meant to be just good enough, meaning it is cheaply built with a low price point but convenient for those looking to shoot OM-mount Zuiko lenses without paying a lot of money. In this regard the OM2000 is worth considering as an option - just as long as you keep its limitations in mind.
The OM2000 has a vertical-traveling focal plane shutter capable of speeds from 1s to 1/2000 (hence the camera's name) along with a Bulb mode and 1/125 flash sync. This shutter is entirely mechanical and is not dependent upon battery power to operate. It is also fairly loud and not well dampened. The camera only offers manual exposure but does display meter readings inside the viewfinder in a simple 3 LED fashion. Metering can be switched between center-weighted or spot, an interesting feature given the consumer/amateur orientation of the camera's design otherwise, but hey it's there. The OM2000 strips out a lot of features - there is no exposure compensation, DX coding, standalone mirror lock-up (it is hidden within the self-timer though) or interchangeable focusing screens. But the OM2000 does have a couple things to give its user such as a mechanical self-timer which also locks up the mirror and stops down the lens to help eliminate camera shake somewhat, the aforementioned spot metering mode, a shutter lock when the film advance lever is pushed in and the ability to do multiple exposures.
The OM2000 is a great embodiment of the notion that with a film camera you really just need a light-tight box to hold your film and a great a lens. The OM2000 is a reasonable light-tight box for just that purpose. Source one of the great Zuiko lenses to mount on this camera and you'll have relatively little to complain about when looking at your final photos.