oh yes, as jth says, storage space: find out how much space your pictures already take up (right click on My Photos or whatever your photos folder is called, then Properties and it should tell you how many gigabytes you're already using), figure out how long it's taken to fill up that many and how many mroe you're likely to need in the future, and buy accordingly....
Doesn't sound like you need much storage space really so a usb flash drive would probably be more appropriate than an external hard drive. It would be more portable and less fiddly to set up. You can get a 32GB one delivered for just £5 (or £8.49 for 64GB)...
I'd not trust memories to a flash drive. Past experience suggests they go wrong too fast, particularly Corsair Voyager types, but others too. If you must use USB flash drives put the data on a number of them and check regularly.
I'm with OG on flash drives and I certainly wouldn't trust CDs or DVDs. If you're hesitating at the cost of a hard drive, think back to the days of film. A 36 exp colour print film will cost you about £5 with a further £5 or £6 for processing. An external 500GB portable hard drive will cost you about £35 to £40 or about the cost of 3 x 36 exposure films, with processing and it will hold about many times your current collection of photos. It's a no-brainer.
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