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If you are in it for medical research, its probably World Community Grid projects you want to work on, then dont worry so much about a graphics card, you want a computer that can run the most CPU threads in parallel as possible.
Right now that is probably an AMD Ryzen 1700 which you should be able to get your geeky brother to overclock (make it go faster).
All the rumours are that AMD and Intel are releasing much better CPUs for this shortly (called i9 and Threadripper) but they may exceed your budget.

To add to what Scalextrix said, you'll find the most interesting or philanthropic projects will often not have the best payout. This is because lots of users flock to these projects, and so the GRC minted per day is split between more people.

Overclocking is a great idea, if you know what you are doing. A lot of people overclock their hardware, and then get lots of computation errors which voids part of their work. You'll have to experiment to see what works best, and may need to look into overvolting. This is especially true for GPUs (and Vortac is the man to talk to if that is your plan).

Our lab is getting several of the 16 core Threadrippers when they are released to replace the CPUs in our workstations. I'll have a play with how they perform on projects like YAFU which has 16 thread jobs and report back.

Hey how comes you get a lab full if shiny new CPUs and I have to buy them ;)

When you have to deal with government grants for many years to fund your research, you become REALLY good at begging. =)

Looking forward to your Threadripper thoughts, Im sorely tempted to liquidate some GRC for some of that action.