Hate to say it, but you're unicorn-hunting. There is no such beast.
Understand that you're shooting a camera with a 2x crop factor. So, a "normal" lens is 25mm. And if you're looking at all classic film-era lenses to adapt to your camera, you're also looking at lenses from an age when 24mm was an exotic super-wide lens. And when f/2.8 was pretty much the fastest most lenses got, so anything wider is also an exotic, and is therefore liable to cost quite a bit more than the $150 you want, even in the "abandoned" mounts, such as Minolta MC/MD, Canon FD/FL, or Olympus OM.
If you have to have f/1.8 or wider, and you can only spend $150 or so, you're pretty much going to be limited to one type of lens, and one lens only, and that would be a 50mm f/1.8 or f/2 kit lens. Which was normal on 135-format cameras, but is going to be a telephoto on a micro four-thirds camera.
Also understand that in adapting your lens, you're going to lose all aperture control from the camera, autofocus, and lens EXIF information (see: Can I use lens brand X on interchangeable lens camera brand Y?). You'll also want to add in the costs of the adapter ring (not some $20 cheapie, if you actually want one with any accuracy of manufacture and decent performance), and the costs of a good CLA for your vintage lens (and you're willing to ignore the whole µ4/3 sensor stack issue). At which point you've probably doubled your budget.
Quite honestly, as someone who adapts manual focus-era lenses to her Canon dSLRs and micro four-thirds gear with wild abandon, it's simply not worth it to save a bit of cash, particularly if you want to go wide-to-normal focal lengths. You do this if you already have collector head and know the ins and outs of condition/repair/restoration (I.e., you laugh hollowly and translate the words "mint condition" on eBay listings to "well I think it's a lens"), and are determined enough to ignore all the myriad inconveniences to get something to work just because they can. You don't do this to get bargains, or to get better glass. You do it to get different glass. But there are so many compromises, you need to be a little nuts to enjoy it. Welcome to the club of crazies if you are.
Honestly? I think you'd probably be best off simply saving the pennies, doubling your budget, and getting the m.Zuiko 25mm f/1.8, so you'll have a lens that's designed for your camera that does everything you want, rather than sacrificing on max. aperture of focal length, and being weighed down with a full-frame sized lens and adapter ring.