I agree, an external USB drive is a simple way of keeping photos offline but if the photos are precious to you. I suggest getting two such drives and copying to both so if one fails, you have a backup.
USB memory sticks are available for a reasonable price up to 128 Gbytes (bigger ones are quite pricy!) and if you say the average photo size is around 5 Mbytes, that would give you space for 25,000 photos. A 1Tbyte external hard disk would give you space for 200,000 photos. A 2Tbyte drive is only a few pounds more than the 1Tbyte so that may be the best in terms or price per unit storage.
I have an external drive for photos, videos and files etc. and a second one as a backup for the important stuff.