Arguments can be made for both. Both can be affected by external environment. I think the better question is, are you going to want to pay for a SSD so that you can stick it in a closet when you can get a HDD for half the price to do the same? I think it would be wise to go with HDD and verify the data once in a while. Again depending on environmental factors, you should get 10-25 years of storage for a HDD or a SSD sitting in a closet. So my suggestion, use the money you saved on not buying SSD (to use as a paper weight) to buy one or more HDD. Redundancy is king for data preservation.
All that aside, if you are only looking to store a couple gigs, just get a couple thumb drives. You don't need to buy Hard drives for a few gigs.