I'm a frequent volunteer troubleshooter on the OBS forums, so if you guys have trouble using OBS, post your log file here (and on the OBS forums) or ping me on either forums and I'll try to help you out.
https://obsproject.com/forum/members/boildown.2086/#postingsFor most games you really want an i5 or i7 (desktop, not mobile) to stream well. Obviously there's little data yet on how well AH3 (or AH2 for that matter) plays with OBS & x264 live encoding. But generally speaking, AH2 should work very well because it only uses a couple threads, leaving most of the CPU available for OBS to use (assuming you've got at least an i5).
And oh yeah, if you want to build a dedicated streaming PC on the relatively-cheap, I highly recommend this guide / reddit thread:
https://www.reddit.com/r/Twitch/comments/47bzdc/budget_friendly_secondary_streaming_pc_guide . I've done it myself and its pretty awesome.
If you only want to capture to your hard drive (like FRAPS but using a modern codec) and you have an Nvidia GTX 6xx series or later, I recommend using the NVEnc encoding option in OBS. This utilizes a separate chip on the graphics card for encoding so it won't impact your CPU or GPU usage. The chip is lightweight as far as encoding quality per bit goes, but you just use a high bitrate and the quality is no different than x264. This isn't a good option for streaming to Twitch, because Twitch's limit of 3500kbps isn't enough to make NVEnc encoded video look any good.
Quicksync encoding works similar to NVEnc, but its somewhat higher quality per bit, but at a non-negligible CPU cost. If you have a Haswell or later Intel CPU, its acceptable even for streaming, as Intel improves Quicksync slightly in each generation. Sandy and Ivy Bridge Quicksync is really only good for saving to hard drive though.
Check out the OBS guides on their web site and forums. 99% of all problems posted on the OBS help forums could have been self-solved by reading the guides and sticky posts.
Also you have a choice between OBS Classic and OBS Studio. OBS Classic has more features and has been out longer, but only runs on Windows (Vista and above) and is no longer in active development. OBS Studio also runs on Linux and Macs, is under active development, but isn't feature complete with OBS Classic yet (though it has a few features now that OBS Classic never received). I personally still use OBS Classic because a plugin I use for my capture card hasn't been written for OBS Studio yet.