1) Drivers:
The LaserWriter IINT is a Postscript level 1 printer, not supported by the drivers built into Mac OS X. Support for these Apple Postscript level 1 printers is available through the driver link below. The software is free (donations accepted) and solid, and half the components have been included with later versions of Mac OS X since the original driver was released for 10.2 Jaguar.
LaserWriter
LaserWriter Plus
LaserWriter IINT
LaserWriter IINTX
Personal LaserWriter NT
http://www.linuxprinting.org/macosx/pslevel1/SupportedPrinters.html
2) Cabling/Highways/Media:
The LaserWriter IINT is equipped with a 0.240 Megabits/sec AppleTalk/LocalTalk port, which you said you have previously connected using PhoneNet boxes and telephone lead-in cords. That wiring can easily be extended to 8 drops and over 1500 feet of wire.
AppleTalk packets can be sent over LocalTalk wiring, Infrared, AirPort wireless, and Ethernet wiring. Most major brands of Hubs and switches will pass them right through, although a few less common brands, especially wireless routers, will not.
The Farallon EtherMac iPrint LT will convert from AppleTalk-over-Ethernet to AppleTalk/LocalTalk. The Asante AsanteTalk does the same basic job. Either of these converter bridges can be had on the used market for under US$25. The AsanteTalk is also available new for about US$100.
Alternatively, if you have an older Mac with both Ethernet port and LocalTalk/Printer/Modem port, you can try a free but unsupported Apple program called "LocalTalk Bridge" that can run in the background on an older Mac and provide the same capability.
If you have an older Mac running 7.5.3 or better, you can use any of these bridge solutions to allow File Sharing with a newer Mac. (10.4 Macs face a few restrictions, and Macs running systems older than 7.5.3 have some restrictions and the setup is harder.)
3) What else you get for free:
When you implement one of these solutions with more than one Mac, you realize the full potential of that printer as a Network printer. It is available to every Mac (and PC if you work at it) on your connected network, and does not require some other computer to be on to print.