Good Intro Editor that can Join Audio+Video, and Present Two Frames Simultaneously
Possible duplicate of: What Beginner Video Editing Software Should I Use?

Though still valid on its own for requesting a specific feature set.
Even though pretty much any video editor will have your requested features.

I often recommend Lightworks (also available for Linux and Mac) as its free and soon to be open sourced.
Here a video tutorial on how to do a so called PIP (picture in picture) effect in Lightworks, he make a split-screen buts its essentially the same workflow, you just allign the videos differently.

Photoshop Elements has very limited video editing capabilities. Nice to have if you own it but if all you need is a video editor I recommend go with Lightworks.

A professional software that is affordable if you work on a project to project basis and not all year long is Adobe Premiere, Adobe has a subscription model where you can rent software for 20$ per month or 30-40$ for a whole suite.
If you don't plan to work on a semi-professional level at some point I recommend you go with the free Lightworks, it has more than enough features to make professional videos, it's just not at convinient and fast as Premiere.