This site has filter sizes for all M43 lenses:
In general it's good to buy multicoated filters. There are many brands, personally I've mostly bought Hoya whose cheapest line of multicoated filters is branded "HMC".
Without multicoating the chance of image degradation increases markedly.
|.....the ROYAL LOTUS 2017/08/25-NEW YORK..... by Chiwat|
from Wild flowers
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from Another cup of coffee