Foot print, smallest shoe size possible?

this is then very high level task.

There is big difference between not leaving any personal data behind and not leave any information at all.

You leave behind information like what software you were running, what files did you open in which order, what make and serial number of usb stick have you been using etc. This is simply a windows function, there is not much one can do about.
It might be slightly better on linux in some aspects, but this will depend on distro, since some of such 'features' are more related to convenience of usage of the graphical front end of the linux rather then the linux operating system itself. (linux itself has no graphical user interface)

>What about using control + C and control + V for copy paste. Does that stay on your clipbrd even if it is done in portable apps open office writer or similar?torbrowser bundle for gathering information on the web and I do it in a cyber caffe on their computer. Will other visitors be able to see what I am doing? Will admin be able to see what I am doing?

is basic windows feature, nothing to do with any windows application, nor open office writer or similar.
Clipboard is windows software and as such it is same for all programs run on windows. It can be run multiply, but mostly it is used only for single copy-paste procedure.
It is however in current windows also user connected, so once user is logged out, computer off, the data is not present just so simply. If you use a computer which does not belong to you and you leave things in clipboard and do not clear the clipboard, it is entirely your personal fault when the things remain there. So it is only your responsibility to clear windows clipboard when you leave the computer. I mean everybody who uses a computer since windows 3.x knows how to clear the clipboard, so this should not be an issue or is it?

BTW: also current GUI for linux have clipboard function, it is not part of the linux itself, but rather of the graphical part like gnome or KDE.

>>**What if I log in my account on a web site that does not have SSL, copy the data from there and log out?
Will the admin or other users be able to see that or will it be encrypted?
Data?
Password, username?

Um... this changes things. The instant you connect your work computer to the work network, they can watch everything you do. It doesn't matter if you are using portable applications, or if you loaded them from your USB drive, or if you use cleaning programs afterwards. They can watch you make every keystroke, they can watch every site you visit, every file you touch.

Please, if work wants you to work while you are on the timeclock, and will fire you if you use company time for your own pleasure, you can't use portable applications or us to help you.

I've said this before... if you don't like your job enough that you need to break their rules, you should find some other employer before they realize you don't like your job and find a reason to fire you, computer use or not.

As I've seen on this site many times, we do not support or intend anyone trying to use PortableApps to get around the rules of your employer.
If you find that PortableApps allows you to do your job better, it's up to you to clear it with your boss. Trust me, a job is a great thing to keep.

A term you will also see in connection with this idea is stealth.
Stealth apps are semi-mythical apps that are undetectable by anyone. I have never seen a truly stealth app. Even if you use a Live Linux CD to boot a computer, it's still possible for a talented IT group to detect that an unexpected OS is running on the network.

Portable Apps are designed not to leave personal data behind, but have never been stealth.

the basic is, that what ever you do on your compute is first considered 'public', that means anybody at least in the same network, can see exactly what you are doing, read any text, knows what you are connecting to on internet etc.
If the other people on the network don't care, the IT admins don't care, then they will not read anything. But they can, any time if they wish.

But you have to adjust the usage of the computer at work so as if they read and see **everything**. That is the consideration you start with.

4 months ago, I started work for a company, we repair and design electronics toys 'for big boys' which are later painted in kind of green color...

Well I can tell you: connection of any usb stick other then one given from the IT department is registered, alarm is given in the IT department 80km away, my boss will get warning mail next day, saying that unauthorized usb devices were detected within his department in company network. We have thousands of computers, workshops and offices scattered throughout the country. Still all that is registered and also exactly supervised.
Our copy/scanning machine is connected to network, when I try to copy some schematics or similar document without asking IT for authorization, the copy machine simply freezes and does not do anything until reset by the IT dept.

nobody can prevent your boss (or the operator of cyber cafe etc) viewing every pixel on your screen and logging every keystroke on your computer.
If you find a way of doing it, report it to proper gov agency and you might become very rich.

You seem still to confuse all the crypto functions.

VPN is protecting data stream against 'man in the middle', that means someone who just reads the data stream on some cables underway between two networks.
It just connects two networks together. But has to have a server and client, it does not work somehow on itself alone.

Example on use of VPN as you ask:
Me and two friends on work stay in UAE.
Skype not possible, since partially passing ISP filters, but certain destinations of packets are blocked by the ISP and big firewall.

One friend is admin in one big international telecom company there. They have big powerful VPN connection to their HQ in europe.
He opened VPN connection on one of their routers/firewalls and started the service on one of their servers for us.
We this way arranged VPN connection from our accomodation via normal ISP to my friends company network.
The contents of the traffic can not be monitored by 'man in the middle', however the ISP(big firewall) could try to block certain form of packets, but it is not so simple any more.
My friend then routed our traffic via the big company VPN to their servers in HQ in europe. From there it was routed to the normal internet, thus skype servers.

So you see, to use VPN, you need two parts! The server with VPN open on the router and the service running and the client on your computer.

Special case are some commercial services, which use common ports on their servers and 'twist' the traffic then so the client in such case is using some generally open ports but the traffic is kind of encrypted. However since the ip of those servers is easy to find out, it is also not difficult to block requests to such serves.

TOR is just for anonymize websurfing.
On your computer, the requests let say : hallo google, here is weringpeter, please send me list of pictures of...

will be sent somehow as :
hallo torserver 1234, here is 5678, send this request to xxyy55 for me please

(where xxyy55 means the encrypted name google for example)

After this have passed few of the tor servers, it is converted back to its original, namely:
hallo google, here is 'last tor server', please send me list of pictures of...

and passed to the google server.

The pictures are then sent similar way back.

If someone cares, it is possible to try to block contact to tor servers, not very simple but possible. Other friend works at big insurance company, their IT guys seem to be smart enough to be able to block traffic to tor network, they have big list of other web proxies which they block as well etc.

So VPN and such things are really not a tool useful to stop monitoring within same network segment as it will be in a company network, cyber cafe or small home network.

I'm guessing they would use such services/techniques at home, or at locations/organizations that are more apt to "turning a blind eye" such as Universities.

The point is, if somebody is absolutely determined to know what you are doing and they have the resources then they can do it. If that person doesn't care or has only mild interest (little time/insufficient resources/lack of knowledge etc), then you may require only the simplest of tools to ensure some basic security/privacy.

I think we can sum up by saying that if you're afraid of getting caught doing something, then you probably shouldn't be doing it. If you don't care about the consequences then why go to all the trouble at all?