@sanitz
That wonderful age old response to technical questions with subtle parts: "It Depends."
You don't indicate much on your profile, which is fine, but it's the first place I looked to guess your technical skill.
Presuming you have no skill, no resources, and *ONLY* want to kick something around like a private LAN game for a couple of days...
You can start running a game (on Java) and use "Open to LAN", others on your home LAN can start playing RIGHT NOW, and you don't have to spend any money or do anything. But that's only cool if "family" means "sitting with me in my living room."
If you are using Bedrock, they don't even have to be in your home. I'm "XBox Friends" with my young nephew, and he and I can play on one another's games from across the country so long as that game is being played. If he closes it down, I'm "kicked" from the game he's playing, of course. It's very "I don't have to do anything."
#MinecraftRealms is a safe bet to just get started NOW playing among family in your home. Either Bedrock or Java, for a low price you can have up to 10 players at a time enjoying a game that's up all the time, as long as you pay.
As you have more detailed requirements *AND* resources, the "recommendations" change, but without info it's really hard to anticipate.
In my case, I can compile JAVA so I'm using the following:
https://extravm.com/minecraft.php, a hosting provider that does NOT hold your hand like other providers, but is less expensive and I can do my own hand-holding anyway. It's paid for by a friend who plays with us, but otherwise trusts me to handle all the support questions.
#SpigotMC, a "server binary" that takes the Official Java Code and makes alterations to it to better support the needs of a server.
#GeyserMC, (A mod, known as a plugin) allows my nephew playing Bedrock to connect to my Spigot Java server. My wife will be spending a month with her adult daughter, and without a PC this will also be her way to use her Android pad to connect to the game and play on it, if she wishes.
I update the Spigot version... from time to time there are bug-fixes that should be done to the version I run. I do that on my local machine and upload it to ExtraVM. I also make backups, and I can verify those backups work on my machine at home.
I *can*, and I *have* run Spigot on a "headless" (no video) machine at home, but it performs better on ExtraVM, and besides... Comcast really frowns upon that. Don't tell them, though. People I allowed could connect to it from the outside, but you *really* have to have expertise to do it securely. ExtraVM just makes all that fuss go away.
So that's a sketchy overview of what's possible, but without more info on 1) your expertise, 2) your resources, 3) what exactly it is you want to do... Java only? Bedrock Only? Mixed? People not living under your roof? ... Without more info, it's really hard to say.
But I'm here, and I'd be happy to help.
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