I want to get a 2.5" USB HDD just to transfer big chunks of data.

When turned on it'll sit unbothered (no shocks and no vibrations) on a desk. But when turned off it'll get the usual everyday treatment my cell phone has: I won't drop it but it will get transported on foot in a messenger bag or backpack, and sometimes while I run, which means some shock and vibration.

Is this going to be a problem? Will it damage the drive?

It shouldn't damage the drive, the heads are parked and as long as there is nothing shock enough to move the heads, which is hard to do, you should be okay.

But with that in mind, if data or your content of the drive is important to you then you could always get a flash drive and its always recommended to keep a second copy of all the data on the disk somewhere else, just in case you loose it or it snaps in half.

As per ShaneWard when switched off, spun down and parked you'd be surprised just how much abuse drives can take. Depending on what you mean by big chucks I'd consider this an ideal case for an SSD in an enclosure. Drives up to 2TB are now very reasonably priced and your only real concern there would be components dropping off the PCB.

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https://www.usbrecovery.co.uk/

Thank you, both!

As for the price, a quick search shows the cheapest 2TB SSD at 161 USD, and the cheapest USB HDD at 47 USD. The price for the SSD is not that big indeed.