Brands are irrelevant, and push the question away from bioinformatics into the realm of Information Technology. You should reformulate the question in a technical manner, and ask a hardware-oriented stackexchange, or maybe serverfault.

Practically, it is a question of data bandwidth, and what kind of analysis you're doing. How often do you need to read the data? are you going to rewrite it in various formats, or just browse it once.

Look for the fastest connectors. Used to be Firewire800, now probably USB3 or eSata. Which does your computer support? Which does their end support? Do you want to use the LAN? Maybe a gigabit ethernet to a mini-NAS would be better, as it can internally RAID the data too.

It raises a lot of questions. If they refuse to upload it to a cluster, what makes you think you'll be able to download it to a laptop? What's the difference between those things?

For the fastest connection between your Mac and an external drive, use a series of Thunderbolt or Thunderbolt 2 enclosures for SSD drives (example).

To give some idea of relative scale, Thunderbolt 2 is about four times as fast as USB 3. Either Thunderbolt or Thunderbolt 2 will have a direct connection to the Mac's backbone and so will easily saturate the pipe between SSD and whatever data is coming out of your Mac's processor.

Thunderbolt + SSD is not at all cheap, but very, very fast. If you need more storage, you can put two drives into a (striped) RAID 0 array via Disk Utility.