So I just discovered something I didn't know as a very new GM. There is a metaplot (are metaplots) that are not part of the SR missions series. I don't know why, but I just assumed that the missions series was the metaplot for the series. Since I was wrong, can someone point me in the right direction of finding the source for the important metaplots of the last few years that aren't from the missions?

Also, I was planning on running my groups through the SRM season 4 as a run up to jumping into 5th, but now I am wondering if there are some good modules that are not missions-based that would be good as well. Suggestions?

The artifacts metaplot starts in the Dawn of Artifacts series but you sure as hell don't want to do those with new characters. For that matter, there are certain Season 4 missions that are pretty damn tough too (I'm looking at you Copycat Killer and Brothers United).
For our latest campaign we did the New York Missions (season 3) first and then moved to Seattle, did a bit of the missions (season 4) there, then Dawn of Artifacts series and then finished up the Seattle missions (season 4).
There are plenty of other adventures that are non missions based you can dive into for more metaplot stuff, like Jet Set (one of those is setting up the upcoming matrix changes for 5th), the Horizon series, Corporate Intrigue (setting up Ares downfall), etc, etc.