By the 'you' I mean the person who does the attack, I'm used to typing 'you' as whatever I'm talking about.
I don't condone crime etc. etc.

I will first try to analyse the problem, methods of proving identity to consider, then consider ways of achieving the goals in the synthesis.

My analysis:

Goals:
1. Gathering account credentials from foreign machines

OP's proposals:
1. Autonomic keyloggers with internet communication ability

Methods of proving identity:

1. Most modern academic labs involving computers have remote logging and remote viewing of all computers connected to network with higher priviliges than the user of the machine. They will definitely gather information regarding which computer was infected, when it was first ran, who was legally in the lab at the moment of infection, who was this seat assigned to, fingerprints on the keyboard or case. Some might not allow unknown programs to be ran, or they would not have admin priviliges rendering them useless, beware of some universities having software that immediately and automatically reports suspicious activity to the network admin. You would be immediately screwed unless you are able to immediately destroy evidence, so I would carry an encrypted pendrive. It might be reported when Windows detects a keylogger .exe because it will recognize it easily once it is decrypted.
1.1. Timestamps - you will be timestamped and the time of execution is tied to the time when you got a computer class. If you do it in more than one room they will have a combination of 2 or more instances of someone doing it. Both timestamps of first time running the program will narrow down possible culprits to you. I don't believe that installing it in 2 rooms is sane, or during two separate courses. It is an instant giveaway of yourself. Not more than one room, and not more than one course is to be fucked! Otherwise you are getting fucked hard. Do not be too greedy and ever attempt it.
1.2. Lack of other suspects - the PC of first contact could be tied to you. Firstly because your person was legally present during the class of first contact with the virus (otherwise you have to break into the room which is an instant giveaway when they check cameras - don't ever do it), secondly because if seats are assigned to people it would be tied to your seat and your seat to your name, thirdly if you use another computer they might check fignerprints if it gets reported to the police and you cannot refuse getting fingerprinted - the virus must be ran directly as a macro from the USB drive to avoid your body's contact with the computer but then how do you decrypt something without touching the keyboard? Maybe unencrypted is the way here but it is riskier.
1.3. You might be spied on - the teacher might be watching your screen at the moment, another student, a camera inside the class or a remote screen sharing program would stream it to the PC of the teacher and he notices too many windows popping up and disappearing. You will either be approached by the teacher immediately, or someone might snitch if later questioned and point to you. They might be logging each program starting and giving instant notifications to the admin if something weird is going on. Very risky, pretty much no way to avoid this problem.

My synthesis:
I assume the goals as the minimal potential, but I will expand them to the maximum damage with no real extra effort. Prioritizing base goals.

If one is to put keyloggers on the computer it would be tied to physically plugging it in and running because I don't believe anyone exploits holes in the code remotely, it is too hard these days.

1. It seems most safe to pick virus type to RAT and not a general keylogger if there is nothing preventing the program from executing with admin permissions. It must be ran from a USB drive which best should be a macro to pull it out fast and without fingers touching the PC itself. I would let the RAT incubate for a few months. It is best that the RAT incubates with no interference with network for some time, then creates its own duplicate and deletes the original along with wiping the memory clusters involved afterwards and enables its duplicate as an autostarting program at boot, so that the original infection date is debatable in court and would raise doubts about your charges but it still is functional. Before the data mining it seems rational to try backup the RAT on other devices, so a spread. I would be prepared though. It might be autodetected and block communications and alert the admin, risky but no organization besides the government does that really. In terms of gaining control it is always best to try to elevate your permissions before roaming loudly and getting detected. RAT would need to take a better protocol as its means of communication with its owner, like TOR. To upload shit safely I think the RAT would serve as a VPN and your RAT is behind TOR. Nobody would bother tracing it, so leaking data is safe assuming that another link doesn't go to the culprit.

Necessities:
1. Prepare an appropriate program and drive - a USB drive is good enough, program should be a decent RAT and not plain keylogger, RAT can do that and much more, RAT can control entire networks besides spying on their information. Getting a RAT and a macro to run and set it up instantly is the best combo as far as my knowledge goes.
2. Get to the computers - I wouldn't specify how to gain access to them and install stuff, it is case dependent. Physical contact is usually needed but it carries the above risks.
3. Infect - case dependent, plugging in the USB drive would be enough if there is a macro with a ready RAT assuming that it gets sufficient permissions, does not get denied execution and doesn't get detected soon after.
4. Have connection from the infected PC to yours - figure out a way to connect over some network to it like TOR, I would make sure if I can run TOR on the network of the infected PC before I attempt it, it might turn out that the admin has prohibited his network from interacting with IPs of the TOR network.
5. Extract infected data - detection would possibly happen soon after, a coordinated extraction from all machines at the same time would be optimal.
6. Upload the gathered data - the easiest part, when it gets to the hackers computer it remains there possibly forever, instant upload is not necessary, I would use an antenna and connect to some free or unprotected wifi to do that.

Other tips:
1. Have all drives encrypted, no exceptions, even your USB tools!
2. When questioned stay silent, don't dig your own grave.
Talking and getting proven lying afterwards which is a punishable offence.
Investigators will analyse every bit and every nuance of what you said, it might lead them to things that only the culprit could know and you are the culprit. It is self incrimination by proxy and idiocy! Stay quiet.
During questioning you stay silent and put your face on the table and hide it with hand so that you don't see your reactions to charges. Stay in one position throughout the entire duration of questioning so that they don't have the ability to tell what you reacted or not to, not giving them a suggestion whether it is you or not. Your body language sells you, do not move. Head to the table, mouth shut, face hidden, and freeze.
3. Do not own anything that can prove to the court you are into computer science. You can't commit a very complex crime with no basic understanding of how they operate! Get rid of that antenna too.

I'm a n00b at this kind of things, I personally never attempted any so it is just my unexperienced theory.
I never proofread because I am too lazy.