I personally use and recommend nextcloud. I choose it due to licensing (nextcloud is 100% open source, whereas owncloud has an open source edition with the enterprise edition being propietary).

Besides that, the main difference between owncloud/nextcloud is that owncloud feels more "enterprise" oriented and offers its professional service as a 1st party SaaS, while nextcloud offers the service mostly through partners (like Hetzner, Ionos, Fujitsu...). However in both companies the 1st party services are quite "big" and expensive for most of us mere mortals (minimum of 25/100 users, with pay per user). You probably will have enough with self-hosting or 3rd party providers.

Also although in the past it took a while for nextcloud to really differentiate itself from owncloud and gain traction, currently nextcloud development moves REALLY fast, which is a great thing for its capabilities (but a bit of extra work and headache to maintain a self hosted instance up to date), and the software has improved drastically in the past years.

From what you are describing, hosting your own nextcloud seems to fit your needs perfectly. Since you also seem to need websites, maybe a VPS instance with tons of storage where you deploy and manage your own service? If you go this way, as other have commented, I would recommend learning and using the docker images, since they will make your life easier in the long run, and will help with the websites/nextcloud living together happily in harmony.

However, for security, I personally recommend to separate the hosting and nextcloud services. I use a managed nextcloud instance (for ease of mind: someone else takes care of the updates, back-ups and security of my storage), and then the website hosting in a different service, so if I make a mistake in my web server I don't risk my personal or family files. I have experience and currently recommend Hetzner for the NC instances (Storage Share), but also have worked successfully with Scaleway using a compute instance to self-host nextcloud, linking it to their Object Storage for the filesystem.

With NC you can create subdomains, assign users and set quotas, define what they can do or not (like for example, sharing files or folders outside of the instance, for how long, allow public uploads...), lock down the instance with 2FA and IP filtering... Nextcloud is really customizable, and has a lot of possibilities if you want to extend it through the apps (like collaborative document editing, or audio/video conference). I have used it for several years with the clients in Linux, Android, Windows, and once you configure it as you want, it simply works.

Good luck!