It depends on your lan size.
Routers are usually support smaller number of concurrent users as they are more specific for handling packets from other networks (normally in this case the internet). If your network requires access to the internet or wireless networking then you can just connect a router to a switch.
Switches can vary in size a lot, but if you're not a particularly large lan or a lan with complex needs then an unmanaged / web-smart switch would probably suffice. For the larger switches, just check that they can actually handle the load at full duplex (i.e, a 16port switch 10/100/1000 should have a few GBps backplane).
If you're planning to host larger lans (above 16 people), then you may want to plan how you want to handle your network. Typically you would have one large backbone switch which then branches out to children switches. With this setup it is difficult to provide full gigabit cheaply as you'd need large trunk branches ... but providing 10/100 is easy with this setup.
If your lan is mostly gaming, then 100mbps is more than enough (considering that we often play on internet connections that are much slower than 100mbps). If you plan to file share, then 1000mbps is better (since it provides about 120mb/s) but 100mbps is fine (12mb/s).
Chaining lots of small switches is okish for small lans since it's cheap to do, but these days its easy to just buy a large switch to begin with.
Unless you know what you're doing, try to avoid Layer 2 and Layer 3 switches for a small lan. Layer 2 is somewhat affordable, but Layer 3 isn't likely to be affordable. These switches are more intended for coporate networks.