I would suggest three 10/100 switches, interlinked with fiber. There are many switches out there with a fiber interface already integrated into the package. This will keep the inter-switch communications from becomming a potential bottleneck.
If you do not require managed switches, you can find these devices relatively cheap by searching the www. Managed switches are quite cost effective as well.
As far as sepparate and interconnected LANs, this can also be accomplished with switches that support VLANs and port trunking. If you have no experience with routers, and want to accomplish this task yourself, I would go the switch route if you are not trying to interface with the outside world.