OMG VIDEO EDITING STUFF //shot
I have not finished a PV before, but that's because I never get content with my work. I do have a lot of practice though!
For NLEs (think Adobe Premiere replacement) I'd definitely recommend either Lightworks or DaVinci Resolve. Both are commercial programs with free versions. Lightworks is what I usually use for video assembly, and it's fast, stable, fast, pretty, fast, flexible, did I say fast? The free version is limited to 720P though, and you need to log in to your account every 7 days to renew your free license, but it's worth it for me. Resolve is limited to 4K (which isn't limited to me at all!), but if your PC isn't top-spec, I wouldn't recommend it for regular use since it uses up a lot of resources.
For compositing programs (suuuper useful for making advanced PVs) , my #1 is Blackmagic Fusion 7. Some say Fusion is more advanced than After Effects due to its node system, advanced 3D rendering features and flexibility, and I'm glad it's now for free, provided you don't need studio collaboration features and stuff like that. I used it to animate this thing for school: (sorry it's in 480P, I uploaded it as a preview and quality didn't matter at the time)
Another compositing program to consider is aviutl, fairly popular in the vocal synth community and kyaami uses it for some stuff.
The above definitely have a learning curve though. But I think it's worth it, and I'd rather use any of those over most of the other free video editors, some of which are so limited and give you ads for the full version that I'd rather use Movie Maker.
Good luck!