Many people seem to be afraid of mixing stable with testing, but frankly, testing is fairly stable in its own right, and with proper preferences and solution checking, you can avoid the "stability drift" that puts your core packages on the unstable path.
"Testing is fairly stable??", you ask. Yes. In order for a package to migrate from unstable to testing, it has to have zero open bugs for 10 consecutive days. Chances are that, especially for the more popular packages, somebody is going to submit a bug report for an unstable version if something is wrong.
Even if you don't want to mix the environments, it's still nice to have the option there in case you run into something that requires a newer version than what is in stable.
Here's what I recommend for setting this up:
First, create the following files in /etc/apt/preferences.d:
stable.pref:
# 500 <= P < 990: causes a version to be installed unless there is a
# version available belonging to the target release or the installed
# version is more recent
Package: *
Pin: release a=stable
Pin-Priority: 900
testing.pref:
# 100 <= P < 500: causes a version to be installed unless there is a
# version available belonging to some other distribution or the installed
# version is more recent
Package: *
Pin: release a=testing
Pin-Priority: 400
unstable.pref:
# 0 < P < 100: causes a version to be installed only if there is no
# installed version of the package
Package: *
Pin: release a=unstable
Pin-Priority: 50
experimental.pref:
# 0 < P < 100: causes a version to be installed only if there is no
# installed version of the package
Package: *
Pin: release a=experimental
Pin-Priority: 1
(Don't be afraid of the unstable/experimental stuff here. The priorities are low enough that it's never going to automatically install any of that stuff. Even the testing branch will behave, as it's only going to install the packages you want to be in testing.)
Now, creating a matching set for /etc/apt/sources.list.d:
stable.list: Copy from your original /etc/apt/sources.list. Rename the old file to something like sources.list.orig.
testing.list: Same as stable.list, except with testing.
unstable.list: Same as stable.list, except with unstable, and remove the security lists.
experimental.list: Same as unstable.list, except with experimental.
You can also add a oldstable in sources.lists.d and preferences.d (use a priority of 1), though this moniker will tend to expire and disappear before the next stable cycle. In cases like that, you can use http://archive.debian.org/debian/ and "hardcode" the Debian version (etch, lenny, etc.).
To install the testing version of a package, simply use aptitude install lib-foobar-package/testing, or just jump into aptitude's GUI and select the version inside of the package details (hit enter on the package you're looking at).
If you get complaints of package conflicts, look at the solutions first. In most cases, the first one is going to be "don't install this version". Learn to use the per-package accept/reject resolver choices. For example, if you're installing foobar-package/testing, and the first solution is "don't install foobar-package/testing", then mark that choice as rejected, and the other solutions will never veer to that path again. In cases like these, you'll probably have to install a few other testing packages.
If it's getting too hairy (like it's trying to upgrade libc or the kernel or some other huge core system), then you can either reject those upgrade paths or just back out of the initial upgrade altogether. Remember that it's only going to upgrade stuff to testing/unstable if you allow it to.
EDIT: Fixed some priority pins, and updated the list.
If possible, I suggest you build a new CD yourself and either mail or upload it to someone who can put it in the tray for you. Use a VM to create and test the image until you can get it 100% non-interactive. Remember, you only need the most basic features. A running system with SSH and one user is enough. The rest you can do (carefully) remotely.
I haven't done this with Squeeze yet, but I assume the process is similar. Worst case, you can autoinstall Lenny and upgrade to Squeeze.
You'll need as a prerequisite a preseed file. Use debconf-get-selections to generate this. Start with the output of that command and edit as necessary. See Debian's official documentation for preseeding the installer for any information you need about the preseed contents.
1) Download an ISO from Debian.
2) Mount and copy the CD contents
mount -o loop debian-508-amd64-netinst.iso /mnt
mkdir ~/autoinstall
rsync -a -H --exclude=TRANS.TBL /mnt/ ~/autoinstall/
3) Edit isolinux/isolinux.cfg and replace the entire contents with the following:
default install
LABEL install
kernel /install.amd/vmlinuz
append vga=normal initrd=/install.amd/initrd.gz preseed/file=/cdrom/preseed.txt debian-installer/locale=en_US console-keymaps-at/keymap=us --
LABEL linux
kernel /install.amd/vmlinuz
append vga=normal initrd=/install.amd/initrd.gz preseed/file=/cdrom/preseed.txt debian-installer/locale=en_US console-keymaps-at/keymap=us --
prompt 0
timeout 0
4) Place your preseed data in the root of the CD image (in this case ~/autoinstall) named preseed.txt.
5) Build the image.
cd ~/autoinstall/
mkisofs -o ~/autoinstall.iso -r -J -no-emul-boot -boot-load-size 4 -boot-info-table -b isolinux/isolinux.bin -c isolinux/boot.cat ~/autoinstall/
You can now use the image to boot from for a VM. Anywhere the installer asks you a question, add that answer to the pressed.txt file and repeat steps 4 & 5.
Keep doing this until you have a viable installer. You'll likely build 20-30 images while tweaking your preseed file until you get it right. Make sure you include openssh-server in pkgsel/include and you should be able to remotely log in.
Best Answer
"Installing Debian GNU/Linux from a Unix/Linux System" from offical Debian documentation.