Just to be absolutely clear:
In your case you get an external IP ddress from your ISP. That is an IP address that is connecting your home network to the internet, and if needed is the IP address you need to get to services hosted on your local network.
Then you have the internal IP address. This is the gateway for your NethServer RED interface. You have configured RED as DHCP client, so this will be assigned automatically. Personally I would go with a fixed IP address for RED if you have services running on NethServer that must be accessible from outside your Local network.
Finally the Green interface. This must be a fixed IP address and must be on another subnet than your RED interface.
You have 192.168.0.0/24 as subnet for your RED interface. You mentioned 10.10.0.0/24 as subnet for your Local network. This is completely fine since this is a private network range.
Now the IP address for your Green interface. You can choose any IP address in the chosen subnet. So, any IP address between 10.10.0.1 and 10.10.0.254 is good. I would go with the first available: 10.10.0.1. The IP address of the Green interface will be the Default gateway for your local network.
2nd Step to configure is DHCP on your NethServer, so NethServer can have the role as DHCP server.
It is a good habit to leave the lower IP addresses reserved for fixed IP addresses on your network. Think of a printer, an accesspoint for WIFi, a managed switch etc...
Go in server manager to DHCP and set DHCP active on you Green interface. The scope of your DHCP range (the first to the last ip address that DHCP may give to clients) can be as you showed in your picture, but then you use up all the IP addresses in your subnet for DHCP. For a home situation there is absolutely no need for so many IP addresses, and as I said before, you might want to reserve some addresses for fixed IP addresses.
So my suggestion would be to choose as start address: 10.10.0.50 and as end address 10.10.0.200
The idea is to have all your fixed IP addresses in the first 50 and if you ever want to play with Virtualbox or another virtualization solution, you have the addresses 201 - 254 to use for virtual machines. This is A option, you can choose any option you want as long you keep your fixed IP addresses separated from the DHCP scope.
I tried to explain as simple as possible. If you have any questions just ask.