Reddit mentions of Lenovo ThinkPad T61 7658 Notebook

First, this sounds paranoid and ill and I would think seriously whether I would want to work there. This reeks of a toxic level of control.

Firing somebody after reading through personal emails would be illegal in most countries and you could consult somebody knowledgeable in labor laws. In general, it is a personal matter what somebody does outside of work. At the workplace, they can require about anything with reasons of data security. But given this, it does not make sense to forbid encryption - it should be encouraged.

What I would do is a very strict separation of personal and work matter including never bringing anything personal to work. This is also the professional thing to do as you do not want to expose patient data to any risk from your leisure activities. That said, encrypting anything that is remotely linked to highly personal medical data and could be lost is a pretty professional attitude and I congratulate you for that. Most health professionals do not take into account how damaging a leak of medical information can be for their patients.

Further, the "Advice" on encryption is mostly bullshit. If you use LUKS, you have a pretty standard way which any major Linux distribution can access. You need, of course, backups, but you can use tar and encrypt them safely by piping them through GnuPG. Also, current file managers such as for Ubuntu or Gnome can open encrypted folders without any effort, you simply have to type your password into a dialog window. All in all, the issues described there are mostly FUD. One issue is that usually, the boot loader as well as the kernel and the initial ramdisk in /boot are usually /not/ encrypted, you would need hard disk encryption to secure their integrity. I think the best source there is to read the Arch Linux wiki but you can be quite confident that today, distributions like Ubuntu or Debian get it right.

If you need to use the same machine for work and personal stuff, I'd suggest to use an encrypted removable hard disk (such as Lenovo Ultrabay) to store your private /home, and leave it, well, at home.

Regarding the cheap laptop, I wouldn't use it. There exist commercial BIOS firmware modifications which are marketed as anti-theft software. They are basically backdoors. Something like that:

http://blog.coresecurity.com/2009/08/11/the-bios-embedded-anti-theft-persistant-agent-that-couldnt-response-handling-the-ostrich-defense/

A PC BIOS today can make a network connection without using the OS, and it can install malware into a Windows or Linux file system. You could never be sure that you really control the PC. Of course you can install an open source BIOS if you think this is the best option, but chances are that you can use your time better.

Also, the price you cite is much lower than normal. You can get something like a used Thinkpad for around $200 and it will have good Linux support. If you are really short on money, you could ask people from a local Linux User Group if they can sell or donate an old company notebook. Many companies replace business equipment within a couple of years. Many sysadmins have dozens of unused old computers lying around and would be happy to give them to a smart student.

Edit: Maybe this one could suit you. These things are a few years old but they are business-class devices which have a very good durability and can be repaired very well by normal people:

http://www.amazon.com/Lenovo-ThinkPad-T61-7658-Notebook/dp/B000UDISEW/ref=sr_1_2?ie=UTF8&qid=1422233843&sr=8-2&keywords=Thinkpad+T61

And of course there are other vendors and fabricants which have equivalent options - this is just the first one which comes to my mind.

That is still multiple hundreds of dollars.

For $130 you can get a new http://www.amazon.com/Lenovo-ThinkPad-T61-7658-Notebook/dp/B000UDISEW. If you wanted a cheaper one you could get one from Ebay for even less and get into the sub hundred dollar range.

It's not the most powerful PC but it can handle lightweight GNU + Linux distros easily, has 160 gb of storage, can handle web browsing, documents, and some other small stuff easily.

Another ThinkPad for $200 with better specs: http://www.amazon.com/Lenovo-ThinkPad-X61-12-1-Laptop/dp/B00DOBSKYA

There's tons of other $200 or sub $200 laptops out there but it's hard

I can see people not wanting to bother with GNU + Linux and I'd understand. I prefer GNU + Linux distros because the software ecosystem on Chromebooks can't compare. Especially when GNU + Linux distros can run Chrome and Chromium just fine.