As was mentioned somewhere earlier in this thread, the cost of external hard drives has come way down, so that when you make the purchase, plan to get two of them, one serving as a backup to the other backup..... I agree, too, with getting the largest capacity external drive you can, because even though you might not need 2 TB of storage capacity right now with your current MBP, you will at some point be purchasing a new computer, and that new machine may have a larger capacity drive, depending upon what you choose as configuration and options. You would be using the new external drive(s) with the new machine, too, particularly in the beginning when setting up the new machine.
These days there are only a few manufacturers providing external spinner/platter hard drives and external SSDs, and some provide the same device "under the hood" with different brand names. External drives come in both desktop configurations (need to be plugged in to the wall to provide additional power) and bus-driven configurations (portable, mobile, just plug right into the computer, no additional power needed). I've used G-Tech G-Drives, Seagate, Western Digital and Toshiba and they all function pretty much in the same way. One nice thing about the G-Technology G-Drive brand is that they are designed for Macs and come formatted as Mac OS Extended With Journaling, so that there is no need to reformat the drive prior to using. Other brands are usually formatted in eFAT or some such, which is fine for people who need to be able to transfer files between Macs and Windows machines, but for an all-Mac household it is preferable to simply stick with Apple/Mac formatting. In the past I used Mac OS ExtendedWith Journaling, but now I have switched to using APFS for my devices because that is how my computers are formatted.
At this point in time, yes, it really is a good idea to begin considering the purchase of a newer Mac, as the 2012 one is pretty close to the "obsolete" ranking that Apple assigns after a few years, and this means that parts are not as readily available, etc. New external drives work much better and faster with newer computers, not surprisingly. However, if you buy a brand-new MBP or MacBook Air you will have some additional things to keep in mind -- namely, the ports, connectors and cables. Apple has changed the ports from USB-A (USB 3) to USB-C/Thunderbolt 3 (with the exception of the 12" MacBook, which uses only USB-C but not Thunderbolt). Some external drive manufacturers are taking this into account now and often helpfully provide two kinds of cables in the box with their devices, which makes it much easier for consumers to make the transition. (Seriously, Apple should have been doing this, too, from 2016, which is when they made the switch in ports.) Also one can buy various adapters and such, too. Anyway, this is not the thread in which to go into all that but just thought I would mention it with regard to looking ahead as you are making a purchase now of external drives -- think about not just using the new external drive with the MBP you have now, but with the next one you will have in the future.