Steve@Mac
Although the original Apple IIe Card Owner's Guide (030-4562-A) was all about the Mac LC and System 6.0.8, it became clear in due course that the card had wider support than that. Your link lists the possibilities. There are, however, caveats to consider when choosing a machine from that list. There are two at the foot of the Table in article 8458, one of which Jim cited to you.
You need to be aware that there are other hindrances than obligatory 32-bit operation in the 'host' computer. The LC 575 restriction is a hardware limitation. The Apple IIe Card is a 65C02 Apple IIe within a Mac, working analogously to a DOS compatibility card in a Mac. You will be best off with a 68030
LC machine: any one in the first seven listed; or a
CC, or a
Performa. Any suitable 680x0 machine is there to provide support for the Apple IIe Card's processor to be itself, but not to provide services that the 65C02 cannot use.
If you intended to have simultaneous use of the Apple IIe card and ethernet for transfer of ProDOS files, Jim's other suggestion (the use of AppleShare) for file transfer, by selecting a notional and optional card in 'Slot 7' from within the Macintosh environment, is the preferable choice, especially if you have previously partitioned the Mac's HDD with a ProDOS partition (up to 10MB) for the purpose.
Apple IIe; 68K: 11DT + 4PB; PPC: 5DT + 3PB; G3: 6DT System 6.0.8 to OS 10.4.x