Eco does not work well with Hamachi. A few Hamachi "experts" have reported that thy have done it and enabled connections that what but that its not always been very stable. The servers is very much set up to use port forwarding for internet connections and if you are all on a LAN then you could all connect to Eco easily with using hamachi. The problem is that using Hamachi to make Eco think its all a LAN connection posses issues.
You have two options basically for hosting friends to play. One is if using Steam you can create a Eco Client world that sets up and allows players to connect to you using Steam Invite and Steam Join. The world would not be listed in the server browser so people would need to know when you are in the game playing and so they could use join or receive an invite from you through steam.
The other option is to set up a dedi server either using the Server in the Tools Library or installing through SteamCMD. You will need access to your router and know how to port forward as well as the proper ways to configure your Firewall. If you all on on the same LAN (behind the same router) you should be then able to see the server without having to deal with router settings. But otherwise you would need to do this.
The downside to running a residential server is the bandwidth you have an that often ends up giving you a poor experience for your players which leaves investigating a game server host.
The Wiki has a good Server section about the different ways to set up the servers but other then one example we can not help with router or firewall setups as they are outside our support focus but you should be able to check your ISP support pages for how to do port forwarding if the allow that and your firewall software should have support pages for how to configure it.
You can also get a bit quicker help with server setups in the #Official-Support channel in the Official Eco Discord.