Western Digital are as good as any. Seagate are also OK. A 1TB USB3 WD will set you back about £75. I think desktops are slightly more reliable, unless you want something you can "stick in a safe place", each time.
DECENT back-up software is worth getting, especially if you want to do frequent back-ups of important stuff, and gives much more peace of mind, that you can recover, if you do have "a disaster".
Acronis True Image is generally regarded as the best, at around £35. There are some quite good free ones, like Paragon, but I use Acronis, as I think it's £35 well spent. For instance, you can set it to automatically check your back-ups, once they are done, and give you an alert, if there's a problem.