Can anyone explain which is the first node (by IP address) that a router will connect to a particular server on a network?
(Agree that the framing of the question is very poor)
There is no address bias by any host to any other host, unless programmed specifically by the application.
A DHCP server will give the next address in the configured list of available addresses, unless a specific "reservation" has been made to the MAC address of the requester. The list is created by whoever configures the DHCP server and can be any address sequence, from any block, from any class. It can be two addresses long or two thousand (or more, or less - though less would be exceptionally stupid IMO).
Routers ("real" or SOHO) have to be specifically programmed to connect to a specific address on the other side of the link. The exception is if the interface is set for DHCP (see above).
If there's some question of a router discovery protocol or something similar, you'll need to clarify what you're looking for.