I live in a rural brick home with Starlink internet. I plan to run 2 Ethernet ports in 7 rooms within 1 month. I want to have internet in my workshop 50 yards away.
1. What Ethernet cable, CAT5e or CAT6?
2. Managed or unmanaged network? Brand?
3. Starlink router or new router?
We really need more information, Will you need the extra a managed switch will bring, VLAN's bandwidth limiting, STP (STP is very important).
What speeds over the network are you looking at?
Someone correct me if I am wrong, Starlink does not give you a public IP address and the new units need to be connected to the router via a USB type socket.
So changing it will not be easy, and if you keep it, you may be tripled NAT'ed.
If it was me personally I would use CAT6 as you can always upgrade the hardware on the ends and get better speeds if needed.
As for a switch, I would drop in a cheap branded gigabit switch and away you go, If you need PoE check what you need and what the switch can supply.