Take a look at this thread starting around post 23 (I think–look for amgradmd’s posts): Bridge II to Mac Mini? (via Ethernet)
Modern Mac Minis, and probably PCs, can auto sense the type of connection so either pass through or crossover cables should work.
As discussed in that thread, I used a Thunderbolt adaptor to create a second ethernet port for my 2011 Mac Mini. One port is connected directly to my Bridge II and the other to my router. DHCP has worked fine for me.