I use Sony Movie Studio Platinum 13. It works extremely well for all of your needs. It is a slightly cut down version of Vegas Pro. The downside is rendering is fairly slow compared to Premiere, but there is no subscription. Another good thing about it, is the trial version is the full version usable for 30 days no restrictions.
There are a few versions of this so watch out. You want the Platinum version because it enables advanced editing while the non-platinum version does not. The Platinum Suite version includes some extra tools like DVD creator that isn't really necessary. Another positive thing is that it is available on Steam: http
So for the negatives, rendering is often slow because there is no GPU acceleration for the codecs with any recent cards. Magix just bought Sony's video editor division, I hope this means they will fix the gpu acceleration but I'm not holding my breath. "Smart Resample" is on by default so you have to disable it manually for every video track you use (annoying, no way to turn off this behavior). It will only work with footage that is recorded with a constant frame rate, so getting ShadowPlay footage to work can be difficult sometimes.
Check the Sony site for the trial versions. If you have ever used Vegas, this is pretty much identical.
ed: forgot to add that I use Bandicam for recording.
The included AVC codec can output high FPS and resolutions. Here is a short video on Dark Souls 3 I made for a friend who never played it: It is rendered at 1440p 60fps
Here is an example of a bad render. Note that it is not the editor's fault, but the codec doesn't like this type of footage.
Here is one of The Division showing picture-in-picture functionality, this is the most basic form of it.