@Kerfanto welcome to the beautiful world of NC and it’s community.
This is possible, for sure, as it is one of the basic features of Nextcloud.
that’s pretty much stuff to host on an external hoster. Of course there are offers that will grant you as much storage. But it’ll cost you a dime, I bet. On the other hand I think storing 1TB of data will cost you a little fortune on Dropbox as well. So you need to compare all offers, I guess.
it can be run by homeusers as well. But it would need at least a little interest in the major subject of cloudstorage, linux etc and for sure it’ll need some time for mainting it at times. I dunno how experienced you are as a user. If you are a rookie it sure enough will be easier to get an (paid) account on some webhoster doing all the maintaining for you (like @devnull tol you). If you think you’d give it a try I’d suggest to try Nextcloud AiO which is pretty easy to set up at your home and which is pretty well documented. Though it means a bit of work for you to get the inital setup done.
If you want to get smarter on things around Nextcloud, selfhosting, and such, try our 101-series.
happy nc’ing