I have some (i.e. not extensive) experience on this, so please take my comments as is.
In early 2003, I had to design a system around a FPGA with some kind of Ethernet connectivity. After a lot of considerations, I've choose
something like this.
The choice was motivated by many factors, including cost and availability of user-friendly Ethernet solutions (not that many at the time). There was significant effort in developing and especially validating the firmware, which was rather complex. We manufacture several tens of such devices and they are still in usage right now.
Then, I helped designing a FPGA-only system where the Ethernet connectivity consists in a Xilinx Virtex 4 with embedded PowerPC CPUs and a Linux OS, eventually complemented by a off-the-shelf Ethernet PHY device.
The practical learning of all this is that if you don't want/cannot spend a lot of effort by starting from scratch. You need a fairly good base that usually consists in a CPU, an OS with UDP and TCP/IP capabilities and so on.
Frankly, I cannot see how you can go halfway/basic with the transport layer (TCP/IP or UDP let's say) stuff. It's relatively complex and a custom implementation is bound to encounter problems when connecting to a reasonable-sized network or when transiting through the first hub or switch.
From my perspective, it's not reasonable to start from scratch. It's much more efficient to start with an existing solution, for both technical and cost considerations.
A single-board computer (starting from USD 25) will most likely offer the features, quality and performances you'll need. Use GPIOs to get out of the CPU.
Or choose a FPGA device and a PHY chip; I think that some Ethernet solutions licenses are free in some cases. You will still need a CPU and an OS. It's usually my second preference as it may restrict the implementation choices and will certainly make you spend some time to understand if the licenses you need for your particular eth>cpu>os combination is free or affordable.
Best regards,
Dan