Get an old computer, install Linux on it, and run Nextcloud.

Nextcloud is basically a cloud storage app like Google Drive or Dropbox, but self-hosted.

Your choice of Linux distro should depend on your level of experience. If you've never used linux before, then I suggest using Linux Mint XFCE edition. XFCE provides a friendly graphical interface while not taking up too much system resources.

I don't have any good tutorials that I can link to, but I'm sure you'll find something if you search for "nextcloud linux mint".

Once you can access Nextcloud from within your home network, you should make it accessible from the outside internet. This is probably the most difficult part. You need to dig around in your router's settings to assign a static internal IP to your homserver, then add a port forwarding rule. Again, search for something like " port forwarding" and "nextcloud port forwarding". Once you have that working, you can just remember your public IP address and use that to connect to owncloud from the outside world. Or, if you have a bit of money, you can purchase your own domain name and use that instead.

It may also be the case that Xfinity does something fucky like assigning an IPv6 address or using CG-NAT. This makes it difficult to make your homeserver accessible from the outside. In that case, I would recommend calling Xfinity and asking for a plain old IPv4 address.

Another consideration is what kind of storage you want to have in your homeserver. The simplest option is to just have one disk (SSD or HDD) with both the operating system and the storage on it. However, keep in mind that drive failures do happen. To keep your data safe, you should make periodic backups to a second storage medium. You can create whole-disk backups using dd, or you can just copy the Nextcloud data directory. The former approach takes up more space, but has the advantage that you can restore the entire system in case of a drive failure, without having to manually re-install linux and nextcloud.

Anyway, this is just the approach I've always been taking. Hope this helps!

Go to the selfhosted community.

You may not actually be looking for a cloud setup (are you de-googleing, and want to host your own calendar and contacts sync?).

If you just want to ensure your photos sync to home, use Syncthing or Resilio.

But I'd still head over to selfhosted, and explain what you want to do - "I have these phones, these users, and this data, and I'd like to ensure that data is sync'd to a home device" - not how you want to do it (the cloud bit - it's not really clear what you need as a solution, just yet).

Also, do you have an off-site backup system for your home devices?

Those folks will have ideas.

Other replies have given you good advice to use as a jumping off point but assuming you are taking data you find very meaningful (pictures and videos) and putting it on hardware you own there are two concepts you should familiarize yourself with asap before going too deep into purchasing stuff and building/installing

RAID: provides redundancy for when a drive inevitably fails. Will require multiple drives to create an array (the amount of drives depends on what kind of raid) but this helps you avoid downtime. Drives will fail, it happens.

Backup: provides resiliency for when your raid array entirely fails so your data isn’t completely destroyed. As you learn about and experiment with raid you may be lulled into a false sense of security, especially the first time you resliver a drive into the array. It’s honestly a bit like magic, you pull the dead/dying drive out and pop in a fresh drive, test it to make sure it’s good to go (not essential but good practice), and then after awhile it’s rebuilt from parity and your data is back. But this process is stressful on the drives and after years of running a home server I’ve finally had an occasion where reslivering caused an additional drive to fail.

Additionally all of the above is pointless in a disaster situation. If there’s some kind of extreme hardware failure that zaps all your drives at once, your house floods/burns down/etc, raid won’t help you obviously at all.

This is where backup gets annoying. If you have 4tb of data it’s pretty inexpensive to create a local backup, a 4-8tb external hard drive (or even larger) can be purchased or made for a couple hundred bucks. Sometimes you can get a refurb 18tb drive under $200 and slap it in a cheap external enclosure.

But offsite for that amount of data is costly and pulls you back into the amazon/google/apple/etc ecosystem, which if you’re anything like me you’re trying to get away from. Another option besides an external drive is a bluray burner and discs. They’re relatively cheap now. I have a different off site backup solution now that I was able to purchase property but the bluray thing was what I did prior to buying land. The downside is that backups were done at longer fixed intervals so there was a risk of losing ~3 months of data. I would burn them and then take them offsite, to a trusted location that I visited fairly regularly.

Ideally you have backups of backups, right? Like putting an SD card in your phone, or a second HDD in your computer. Then the "cloud" part...my recommendation, considering you asked for simplest, is a NAS. Get a user-friendly one with built in apps that can do what you're asking, and you shouldn't have issues

I might get flack for suggesting this, but for what you want, you'll not only need storage, but something to auto save the videos and pictures from your phone - and maybe auto delete old ones that have already synced to cloud when you are running low on space.

Amazon Photos does this. It has apps for iOS and Android that auto upload the photos. You can get a pretty large amount of storage for $99 a year. It's a "set it and forget it" solution for family photos and videos. It also has a bulk uploader tool for Windows to do the initial upload of your current photo/video storage.