Let's get some terminology aside first.
"Fiber channel" (or "fibre channel", as it's more typically known) is a specific networking technology used in storage area networks. I think, when you say "fiber channel", you're really saying "ports on an Ethernet switch that fiber optic cables connect to". If you're really talking about fibre channel then, let me know... (but, to my knowledge, 3Com has never made a fibre channel switch).
The term "stacking" typically refers to an interconnection between Ethernet switches through a (typically proprietary) dedicated interface that extends some significantly high fraction of the capacity switch's switching capability to another switch (extending the "switching fabric" outside the box to another switch). Often, stacking interfaces operate at multi-gigabit speeds (40Gb/sec on the Dell PowerConnect 6200-series switches, for example).
There is no "hard limit" to the number of Ethernet switches in a network. You can add as many as you want. Latency will increase as the number of "hops" between any two endpoints goes up and, obviously, you're increasing complexity and odds of failure as you add more switches.
Switched Ethernet LANs can't scale indefinitely. Excessive broadcasts or flooding of frames to unknown destinations will limit their scale. Either of these conditions can be caused by making a single broadcast domain in an Ethernet LAN too big.
Broadcast traffic is easy to understand, but flooding of frames to unknown destinations is a bit more obscure. If you get so many devices that your switch MAC tables are overflowing, switches will be forced to flood non-broadcast frames out all ports if the destination of the frame doesn't match any entries in the MAC table. If you have a large enough single broadcast domain in an Ethernet LAN with a traffic profile that hosts talk infrequently (that is, infrequently enough that their entries have aged out of the MAC tables on your switches), then you can also get excessive flooding of frames to unknown destinations.
At the scale you're talking about (200 computers), there isn't going to be a problem with flooding of frames to unknown destinations. Whether or not you have broadcast problems will depend on the specific protocols and applications used. If you're using off-the-shelf Microsoft OS's and applications, I'd hazard that your level of broadcast traffic is just fine.
In general, a "star" topology that minimizes "hops" between switches is the most effective Ethernet topology. Placing servers or other highly-utilized resources in the center of the star will minimize traffic overall. If your switches support aggregating multiple links together, you can use this feature to increase bandwidth on inter-switch links. You should be using a tool (even a simple one like MRTG) if your switches support monitoring with SNMP to determine where your bandwidth utilization "hotspots" are.
You can create "loops", provided your switches support the spanning-tree protocol, to handle failures of switches or inter-switch links. That's a little more advanced topic, and not something I'd recommend you approach until you have more experience.