• Netgate 6100.
  Is higher in price but will power saving and powerful running
  with several and different ports.

• mini-ITX Intel Xeon E3-1230v3 with 16/32 GB ECC RAM
  Is here able to get over eBay for 110 € (16GB) or 158 (32GB)
  used but MoBo, CPU and RAM for that price is the bang for the bucket in my eyes.

• Intel N5005 or N6005

Something between 195 € or 225 € without M.2 SSD and RAM, but powerful and 2.5 GBit/s Ports (v3) and fully silent.

The network structure looks like this.

Is the modem port 1 GBit/s and the pfSense WAN Port
also? Or is the modem´s port 2,5 GBit/s and the pfSense
1 GBit/s port "only"?

I am currently using motherboard Odroid H2.
Everything seems to work fine, but the Odroid
H2 has a weak CPU.

Saving power or low power using and routing nearly a full GBit/s line at the wan, firewall rules, and other installed packets could narrow down the entire throughput once or
twice again. Counting some TCP overheat on top you may
be very well sorted, it should be then something around ~600 MBit/s from 800 MBit/s.

I pay for an internet connection of 800/200 Mbps, but
I only get 550/200.

From the site of pfSense, it was announced to get hands
on a CPU with nearly ~ 2,0G Hz to get out around ~500 MBit/s throughput. So your CPU come with 2,3 GHz and
so the ~550 MBit/s will be a good number for your device as I see it, that menas only in my opinion.

I am looking for a new motherboard and CPU.

On top of all above named things, it could be that you are using PPPoE and then you entire WAN traffic is nailed to one CPU core "only"! With PPPoE not in usage the entire WAN traffic is running then over all 4 CPU core or more cores then the one that is used now. So you may be thinking on your next or future hardware will be able
to route a full Gbit/s or plain is beefy enough to do so.

3GHz would be nice if you are using PPPoE to ensure that
you will be not ending up in the same situation again.

mITX gigabyte/asrock etc

• Netgate 6100 would be my choice to serve this.
• Any MoBo with Xeon E3-1230 will do the job
• Intel Core i3, Core i5 or Core i7 would do the job also

minimum 2x LAN intel

• Intel i225v3 you might be looking for
• Intel i226 is supported with pfSense version 2.7

minimum 4x SATA ports

Why not mSATA or M.2? For low power usage and heat?

CPU ultra low consumption Intel/AMD

• Intel "Denverton" C3000 Series
• Intel N5005 or Intel N6005 maybe your choice

RAM DDR4

Is also given with a modern CPU type

Can you advise me some decent HW?

• Netgate 6100.
• mini-ITX Intel Xeon E3-1230v3
• Intel N5005 or N6005 CPU successor of your j4125