I doubt that there are many free software packages that will do the stop motion or green screen. However what she could do is download something like MonkeyJam. It's very easy. (Pretty much plug a webcam in and click "capture.") It's only SD quality but it's great for getting into it.
To use greenscreen you could use WAX 2.0. It's a Sony Vegas look a like from like 2004. it has a keyer into it. You might even find a way to use WAX 2.0 as a stop motion program if she is going to use a webcam instead of a camera. A tutorial on that here.
Normally people would do this in Adobe After Effects (Free alternatives: Apple Motion for Mac users, Wax for Windows users) but you can also use Adobe Animate (formerly Flash Pro) to animate the logo.
To be honest, After Effects is all I use. I imagine most other video software could handle those tasks though.
If anyone else knows another, please mention it.
Wax 2.0. It has a strange interface, but can actually do multiple layer editing, as well as some low-level effects like chroma-key, layer transformations, pen tool, etc. It's no After Effects, but for free its a really nice program, especially for beginners.
Why not start small with a couple of shorts on Youtube?
There are decent free editing apps out there.
I downloaded Wax last night and it looks good enough to start with.
Oh, and there are a bunch of filmmaker reddits as well. --->
Grab a copy of a free video editing program like Wax | http://www.debugmode.com/wax/ | or a trial version of any of the more popular programs like Avid, Premiere, or Final Cut and familiarize yourself with the software. Then, hit up as many tutorial videos as you can possibly endure. Then: http://www.howstuffworks.com/jobs.htm