Ethernet RJ45 interfacing with microcontroller
Your option 2 is only viable if your microcontroller has built in Ethernet hardware. Most controllers don't, but they exist especially at the higher end of the spectrum.

Your option 1 with a separate Ethernet controller is pretty common. You may want to check several open hardware microcontroller boards and get yourself inspired by how they solve Ethernet (and which chips they use). Most of the time circuit diagrams and libraries are fully available, but mind the license that they come with. I know there exist Arduino compatible boards with Ethernet, but I'm not sure of its name.