I picked up a used Oly E-M1 mk I with the Oly 75-300mm last August to take pictures of nature while out on walks and fell in love with it. I should have done a bit more research because I grew out of both camera and lens pretty quickly. That is a fine combo, but I wanted just a bit more. I picked up the OM-1 mk I a few moths ago for $800 on eBay refurbished and haven't looked back. I recently got the 100-400mm used on eBay for $700. I really like the 100-400mm over the 75-300mm, it's the better glass for sure and that extra 100mm has come in clutch. Also the 100-400 is sharper at the long end and has IS. I will say the 100-400 is quite a bit heavier and bulkier than the 75-300. My kit with E-M1 and 75-300 is just over 2lbs and the OM-1 with 100-400 is just over 4lbs. Still I have no problems lugging the new kit around on long walks and usually keep it clipped to one of these clips and its really comfortable.
I love the kit and I think that lens is a sweet spot for weight and capabilities. I'd suggest getting the mk II of the lens though. The new version has OIS that works with the IBIS of the body.