Install Android-x86 in Virtualbox VM, then root it Problem

I want to install Android in a VM to restore a backup using Titanium Backup. For this to work I need Android to be rooted.

What I tried

I've tried to install Android-X86 4.3 in a Virtualbox VM. The installation seems to work. I made a 8GB partition disk (sda1), made it bootable, and installed Android in it from an ISO file. This all seems to work. Android starts, I can browse the internet, install apps, etc. Then I want to restart the VM, and guess what?! I go back to the installation screen, like starting up from the ISO live image. 

For normal stuff I can make a snapshot, start that up, and do anything. My problem is that I need root permission to restore a Titanium Backup in that VM. And I cannot root this VM because the disk is not writeable. With ALT-F1 I become root, and I can use a script to root Android. But my guess is that I'm still on the ISO and that is not writeable. 

Update - another try with Android 4.2

As mentioned in the comments, 4.3 would have problems with root access. I tried 4.4, which didn't start at all. Then I tried 4.2, which has the same problem as 4.3 for me. I made a screenshot of what I see when I try to run the rootscript, which is described here. 

You can see the errors: rm failed - Read only filesystem

How can I fix this? 



My question

How can I install Android permanently on this VM, so it can reboot and then be rooted?
For your reboot problem, it sounds like your boot order is booting off the .iso, i.e., cdrom, before it looks for the disk partition where you installed Android. Shut everything down and disconnect the .iso. You can just delete the CD device under the controller within VirtualBox Settings->Storage. You probably shouldn't just change the boot order or you will have trouble reinstalling if you ever need to. However, if you want to change the order, look under Settings->System->Motherboard.