I have been running Owncloud since 2011 without any reverse proxy and it's been fine.

I'm still on an old version because every time I have tried to upgrade it, it has fucked up, and i've wasted loads of time getting it back running again. New versions /should/ be better I hope!

Pick decent user passwords, protect it with SSL, and have a local firewall on your server that only allows required ports though (80 and 443), and you should be fine.

I take a backup of mine now and again, but it's quite small - only about 50gb.

Nextcloud is more like a "star" configuration, where Nextcloud is the server, with multiple clients. Of course the clients can cache data from Nextcloud.

Syncthing is more like a mesh, where each client serves data to others (although this is configurable),

Nextcloud has way more features, like shared calendars, video conferencing plugins etc, which is great, but may be overkill for your needs.

I use both, although NextCloud/OwnCloud fits my needs better.

I would say syncthing is easier to set up. There is more admin overheard (esp upgrades) with NextCloud/OwnCloud.

If the domain isn't critical if it changes, you could use freedns.afraid.org.

I've been using the free version for over a decade (but did donate recently). A couple of domains have come and gone, so I've had to pick new ones, but it's not a big deal.