Or if you really trust a VPS provider, just pre-pay them way too much money and see if you can get a mutually binding contract that is transferable upon death to a family member to keep the site alive. Co-admins.
Who do you want to see this site? The whole world, children and grand-children of friends and family? If family just put your site and some videos on multiple copies of thumb drives, DVD's and hope adapters exist or that family members maintain copies.
Or, you start by making it a business of some kind. Then you write rules that outline and support your goals, an organization around a website that outlives you by 100+ yrs. You'll need a way to support it so you need a business that will always be profitable enough to keep the website up. A business related to food-stuff or shelter. You'll need a CEO and a board of directors that will carry out your will as time passes and technology changes.
Or, you can create a time capsule where you can place a smartphone plus a power source that can be started 100+ years from now. You might want to print it on some kind of material that does not deteriorate, just in case -- maybe,some kind of plastic with raised letters rather than ink or carve it in stone. Pick high ground to make sure water does not destroy it. You'll need to make a big deal about it so that people will know to open it 100+ years from now.
Or you can make it part of your family mission. Someone in each generation will be responsible to move the website forward. It needs to have very important information so that each generation feels like they are carrying out an important mission. Your family will be the keepers of that information.
You can make the website related to a religion. If it becomes a daily use by the members, they will maintain it; then the site will be up for centuries.
Those are my quick ideas. I'd be interested in what others think up.