A classic Ethernet chip "only" takes care of the Ethernet layer. This means that it's up to the 6502 to handle the TCP/IP layer. IP65 is such a TCP/IP layer for the 6502. Running the TCP/IP layer already takes away quite some resources from the 6502 not available to the "rest" of the running program. The Cirrus Logic CS8900A is such a chip - and the one usually used for 6502 based systems.
However with the rise of embedded systems there were enough systems with limited resource that there was a market to develop chips with integrate the TCP/IP together with an Ethernet (or WiFi) layer. After several rather expensive chips the Espressif ESP8266 and ESP32 are by now THE solution.
With the WIZnet W5100 Ethernet chip there's sort of a hybrid. It allows to be used both as pure Ethernet chip as well as TCP/IP+Ethernet chip.
So what type of chip to go for on what machine?
On the C64 there are quite some CS8900A-based programs. So RR-Net MK3 at the end stayed with the CS8900A used before although there was already a prototype with the W5100.
On the Apple II and the ATARI there are less network programs to be compatible with. Most/all relevant programs are based on Contiki or IP65. And both Contiki and IP65 allow to easily switch between the CS8900A and the W5100 (with the W5100 used as pure Ethernet chip). Additionally the W5100 brings options to develop code using the ESP8622 TCP/IP layer.
On other machines I personally would consider this:
- On a machine with (nearly) 64kB RAM and reasonably well supported cc65 C library I tend towards the W5100. It allows to a) easily bring the existing Contiki/IP65 programs to the machine in question and b) make use of the W5100 TCP/IP layer for new programs.
- On a machine with (much) less RAM and/or weak/no cc65 C library I'd rather think about an ESP8266/ESP32 approach. In contrast to the W5100 the Espressif chips don't contain only a TCP/IP layer but additionally a DHCP client, DNS client and HTTP(S) client.
After these rather lengthy general remarks now for a more specific answer to "what would be the requirements in order to easily interface with IP65?": A CS8900A or W5100 or LAN91C96 with its registers mapped straight to some 6502 memory mapped I/O locations.