Is it safe to move these folders from my boot drive?

The first one with the long hash name is a windows update directory.
Expat Shield is a web access encryption product so it's going ot be integrated into system files.
Nvidia folder is probably fine to delete, i don't remember if it stores any driver update information.
Program files is all of your applications and software, don't delete this.
Users is all of your user directories like downloads, documents,desktop, appdata, etc... Can't delete this.
Windows...is well...windows, so don't delete this lol

But of course if you just want to keep your user data and not windows and the programs and applications then just copy the users folder and format the drive and do a fresh instll of windows on the ssd.

if you can't or don't want to do a fresh install of windows on the ssd, you can actaully use cloning software to make an exact image copy ont othe ssd when you get it. You'll need to make sure that you have less than 27GB of usable space filled in that case, so you'll need to unisnstall most of your programs and expat shield and clear any user documents, movies, pictures, etc....

Also, a 30Gb SSD will only really be able to hold windows and the updates it uses. You're going to have to be aware that any programs you install will need to be on a custom location on a different drive.

So my question is which folders do I have to move to the SSD for it to work?

Well, you shouldn't move the folders individually, because just copying over the windows system files won't gauranty windows will boot properly and not cause system corruption.

You'll need to do what's called "cloning" the drive to the ssd. Basically you're taking a sefctor by sector image of the hard drive including the file system information and cloning it over to the ssd.
As long as the hard drive has less than 27GB of used capacity, you can do this with free software very easily.

Otherwise, you'll need to do a fresh install of windows onto the ssd.

Well, I found a 60GB SSD, so I ordered that one instead. What software can I use to transfer the data from the hard drive to the SSD so I can boot from it?

Can I delete that one?

I would use acronis true image.
That's what I use currently, I'm not sure if it will work with the trial version.
There's also alternative sources you can use.
PM if you have some more questions about that.