Every once in a while, Costco puts 8TB external Seagate drives for sale for $99. They are USB C and very fast. It's a lot of local storage space for very little cost. If you intend to use an external drive as a local backup I would buy a pair drives to back up each other. Otherwise, if you only buy one drive you are rolling the dice that it wont fail.
I can tell you from experience I am glad that I backup up my data because as I progressed in the hobby, it was fun to revisit old data and reprocess just to compare results after learning new techniques or with different software that was previously unavailable to me.
There are various cloud services out there as well. Idrive offers 5 TB of backup space for a year for less than $60 but the price might change after that. It might be a good idea to check out a few cloud services before you decide on one. Some them will send you their drive (once a year for free, or for a small fee) so you don't have have take forever to upload your data onto the cloud over the internet. Just copy the data locally and send the drive back to them. Usually, they will make several copies of the data you upload on that drive once they receive it back from you. Most reputable services store back ups of your data in several different locations in case of fire or natural disaster or some other catastrophic event.
5 Tb might be enough to hold you for a while for all of your deep sky imaging data but that is no where near enough if you want to keep all of your raw data from planetary imaging. You have to decide how serious you want to get about preserving your data first and then examine your options.
The cheapest and fastest way is locally with a pair of external hard drives the more expensive but more secure way would be on the cloud.