This is hobbyist open development stuff here, so no one has bothered with recommended specs, and no one probably will in the future either. The tech changes too quickly, it would be hard to come to an agreement, it would be hard to keep the recommendations up to date, it would vary on too many factors, etc, etc.
I can tell you what I've built that works:
https://www.reddit.com/r/Twitch/comments/47bzdc/budget_friendly_secondary_streaming_pc_guide
If you don't want to bother with ebay and used gear, I'd go for a Ryzen 7 build instead.
If you want to save money, depending on what you want to do, you don't have to go that high end, but we'd need to know more about what you want to do.
Yes, different games have different visual complexities, and so while a card game (HotS) might have no trouble encode on a certain hardware or settings, a more visually complex game (like FPS) might fail on the same.
Another factor is the video capture card. The most general advice is to get a PCIe adapter, not USB. Even USB 3.0 devices have a ton of people posting about problems on these forums. PCIe capture cards are way more reliable.
Oh and like Suslik says, unlike most other recording software, OBS requires a not-terrible GPU to work. Something like a GTX 550 or better, I'd say. If you're buying something new, go for a GTX 1050.