I bought my first OM-1 in 1974/5 - a plain OM1, not the later OM1-MD or OM1n.
I'm currently without an OM1 body, but I do have 4 other OM bodies: one OM2n, one OM2s and two OM-Gs (aka OM20s).
All the bodies I currently own use readily available, current batteries.
The single digit OM bodies are wonderfully compact, but they aren't as light as later, more electronic cameras. I have a couple of Canon EOS film bodies that are a fair bit larger than my OM bodies, but a lot lighter than an OM1n or OM2n.
In recent years while using my recently sold OM1n or OM1 bodies, I used them with two different types of battery adapters.
The first type of adapter is the type that John Hermanson sells on zuiko.com. It allows use of a smaller silver oxide cell in the larger battery compartment of the OM1, and it converts down the voltage to the right amount. There are other sources as well for similar adapters. They work very well, and in something like an OM1, the silver oxide cell lasts for a long time.
The second type of adapter also works well and is less complex, and therefore less expensive. It has no circuitry, but it allows a small hearing aid battery to power the OM1 meter. The hearing aid batteries use the same chemistry as the zinc air cells, so they have the right voltage and discharge curves, but like the more expensive zinc air cells they don't last particularly long. The hearing aid cells are incredibly cheap in quantity and are easily found at drug stores as well as Costco. I bought my adapters from Jon Goodman, who posts here regularly and was formerly active on eBay, particularly with respect to his light seal kits. His adapters are very reasonable in price.
I would recommend that you have John Hermanson service any OM1 or OM1n. As posted above, he will convert the camera to modern silver-oxide batteries (not alkaline, as posted above), and deal with one problem that OM bodies have. The cameras depend on a type of light seal material that can degrade over time. The light seal material that is near the prism is particularly important to remove, and John does that.
FWIW, both my OM2n and my OM2s are very easy to use for manual exposure. They do, however, require batteries for more than the meter, so if battery dependency is a problem for you, they may not be suitable.
You indicate that size and weight of the camera and lenses is important for you. The OM lenses are as compact as the bodies, but like the single digit OM bodies, they are well built and fairly heavy - again in comparison to something like the kit zoom lenses that were sold with some more recent electronic film cameras.
I like to carry a three lens kit with a single OM2n or OM2s body - a 24mm f/2.8, a 35mm f/2 and an 85mm f/2 lenses. The body and lenses together are extremely compact - they fit together into a very small camera case. Those lenses are fairly popular, and can command a premium price on eBay or through other appropriate sources
The OMGs/OM20s are also interesting. They are clearly aimed at the amateur market, but they are equally compact, quite good to use, and a fair bit lighter than an OM1. They aren't as robust as the single digit OM bodies, and they are also battery dependent.
If you haven't already seen it, the so called Olympus OM Sales Information file is your friend for details about the system. Note the links thereon to scanned manuals: http://www.star.ucl.ac.uk/~rwesson/e.../mainindex.htm
Hope this helps.