Ethernet Layout Guidelines
Look for application notes for your PHY and magnetics.  The manufacturer would know best in regards to what works with their parts.

Generally there is no ground/power or routing under the magnetics and try to avoid ground/power under the TX/RX pairs.  If you can't route the whole trace without a ground/power plane under it, leave the plane under it.  It is worse if you go over a break in the plane.

For termination, check with manufacturers of the PHY and magnetics.  Like you said, there are a few different schemes, the manufacturer should know best about their device.

We follow what I described above at work and don't have any problems with ethernet.